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数学研发论坛»论坛 › 【算法研发】 › 编程擂台 › 1/n=1/a+1/b+1/c+1/d
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楼主: 王守恩

[讨论] 1/n=1/a+1/b+1/c+1/d

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王守恩
 楼主| 发表于 2026-2-6 12:37:47 | 显示全部楼层
方向明确：找一个数字串(有无限项), 满足 n 项倒数和(允许 "+" 或 "-" ) = 1。a(n) =  n 项最小和。

先试试简单的。在光滑数(13)里。 满足 n 项倒数和(允许 "+" 或 "-" ) = 1。a(n) =  n 项最小和。—— n 项最小和也不好找。

各位好友！这些数据是否有错？——特别是前面小的是否有错？应该有更小的？谢谢各位！！！！

a(03)=11, 1/2 + 1/3 + 1/6=1,

a(04)=21, 1/2 + 1/3 + 1/4 - 1/12=1,

a(05)=27, 1/2 + 1/3 + 1/4 - 1/6 + 1/12=1,

a(06)=40, 1/2 + 1/3 + 1/4 - 1/5 + 1/6 - 1/20=1,

a(07)=50, 1/2 + 1/3 + 1/4 - 1/5 + 1/6 - 1/10 + 1/20=1,

a(08)=57, 1/2 + 1/3 - 1/4 + 1/5 + 1/6 - 1/10 + 1/12 + 1/15=1,

a(09)=77, 1/2 + 1/3 - 1/4 + 1/5 + 1/6 + 1/8 - 1/10 + 1/15 - 1/24=1,

a(10)=84, 1/2 - 1/3 + 1/4 + 1/5 + 1/6 + 1/9 - 1/10 + 1/12 + 1/15 + 1/18=1,

a(11)=99,  1/2 - 1/3 + 1/4 + 1/5 + 1/6 + 1/7 - 1/10 + 1/12 + 1/14 + 1/15 - 1/21=1,

a(12)=116, 1/2 - 1/3 + 1/4 + 1/5 + 1/6 + 1/8 + 1/9 - 1/10 - 1/12 + 1/15 + 1/18 + 1/24=1,

a(13)=126, 1/2 + 1/3 - 1/4 + 1/5 + 1/6 - 1/7 + 1/9 - 1/10 + 1/12 - 1/14 + 1/15 + 1/18 + 1/21=1,

a(14)=146, 1/2 - 1/3 + 1/4 + 1/5 + 1/6 + 1/7 - 1/8 + 1/9 - 1/10 + 1/14 + 1/15 + 1/18 - 1/21 + 1/24=1,

a(15)=158, 1/2 - 1/3 + 1/4 + 1/5 - 1/6 + 1/7 + 1/8 + 1/9 - 1/10 + 1/12 + 1/14 + 1/15 + 1/18 - 1/21 + 1/24=1,

a(16)=178, 1/2 - 1/3 + 1/4 + 1/5 - 1/6 + 1/7 - 1/8 + 1/9 + 1/10 + 1/12 + 1/14 + 1/15 + 1/18 + 1/20 - 1/21 + 1/24=1,

a(17)=196, 1/2 - 1/3 + 1/4 + 1/5 - 1/6 - 1/7 + 1/8 + 1/9 + 1/10 + 1/12 + 1/14 + 1/15 + 1/18 + 1/20 - 1/21 + 1/24 + 1/28=1,

a(18)=224, 1/2 - 1/3 + 1/4 + 1/5 - 1/6 + 1/7 + 1/8 + 1/9 - 1/10 + 1/11 - 1/12 + 1/14 + 1/15 + 1/18 - 1/21 + 1/22 + 1/24 + 1/33=1,

a(19)=244, 1/2 + 1/3 - 1/4 + 1/5 - 1/6 - 1/7 + 1/8 + 1/9 + 1/10 + 1/11 - 1/12 - 1/14 + 1/15 + 1/18 + 1/20 + 1/21 + 1/22 - 1/24 + 1/33=1,

a(20)=272, 1/2 - 1/3 - 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 + 1/10 + 1/11 + 1/12 + 1/14 + 1/15 + 1/18 + 1/20 - 1/21 + 1/22 + 1/24 + 1/28 + 1/33=1,

a(21)=302, 1/2 - 1/3 + 1/4 + 1/5 - 1/6 - 1/7 + 1/8 + 1/9 - 1/10 + 1/11 + 1/12 + 1/14 + 1/15 + 1/18 + 1/20 - 1/21 + 1/22 + 1/24 + 1/28 + 1/30 + 1/33=1,

a(22)=336, 1/2 - 1/3 + 1/4 + 1/5 - 1/6 - 1/7 - 1/8 + 1/9 + 1/10 + 1/11 + 1/12 + 1/14 + 1/15 + 1/16 + 1/18 + 1/20 - 1/21 + 1/22 + 1/24 + 1/28 + 1/33 + 1/48=1,

a(23)=366, 1/2 + 1/3 - 1/4 - 1/5 + 1/6 + 1/7 - 1/8 + 1/9 - 1/10 + 1/11 + 1/12 - 1/14 + 1/15 + 1/16 + 1/18 - 1/20 + 1/21 + 1/22 + 1/24 - 1/28 + 1/30 + 1/33 + 1/48=1,

a(24)=401, 1/2 + 1/3 - 1/4 - 1/5 + 1/6 - 1/7 - 1/8 + 1/9 - 1/10 + 1/11 + 1/12 + 1/14 + 1/15 + 1/16 + 1/18 + 1/20 + 1/21 + 1/22 + 1/24 + 1/28 + 1/30 + 1/33 - 1/35 + 1/48=1,

a(25)=437, 1/2 - 1/3 + 1/4 - 1/5 - 1/6 + 1/7 + 1/8 + 1/9 + 1/10 + 1/11 + 1/12 - 1/14 + 1/15 + 1/16 - 1/18 + 1/20 + 1/21 + 1/22 + 1/24 + 1/28 - 1/30 + 1/33 + 1/35 + 1/36 + 1/48=1,

a(26)=477, 1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 - 1/8 - 1/9 + 1/10 - 1/11 + 1/12 + 1/14 - 1/15 + 1/16 + 1/18 + 1/20 - 1/21 - 1/22 - 1/24 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/40 - 1/48=1,

a(27)=518, 1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 - 1/8 + 1/9 - 1/10 - 1/11 + 1/12 + 1/14 + 1/15 - 1/16 + 1/18 + 1/20 - 1/21 - 1/22 - 1/24 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/48 - 1/54=1,

a(28)=531, 1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 - 1/8 + 1/9 - 1/10 - 1/11 + 1/12 - 1/13 + 1/14 + 1/15 - 1/16 + 1/18 + 1/20 - 1/21 - 1/22 - 1/24 + 1/26 - 1/28 - 1/30 - 1/33 - 1/35 - 1/39 - 1/48 - 1/52=1,

a(29)=567, 1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 - 1/9 - 1/10 - 1/11 + 1/12 - 1/13 + 1/14 + 1/15 - 1/16 + 1/18 + 1/20 - 1/21 - 1/22 - 1/24 + 1/26 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/48 - 1/52=1,

a(30)=607,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 - 1/9 - 1/10 - 1/11 + 1/12 - 1/13 + 1/14 + 1/15 + 1/16 + 1/18 - 1/20 - 1/21 - 1/22 - 1/24 + 1/26 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/48 - 1/52=1,

a(31)=648,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 - 1/10 - 1/11 - 1/12 - 1/13 + 1/14 + 1/15 - 1/16 + 1/18 + 1/20 - 1/21 - 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/48 - 1/52 - 1/54=1,

a(32)=688,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 - 1/10 - 1/11 - 1/12 - 1/13 + 1/14 + 1/15 + 1/16 + 1/18 - 1/20 - 1/21 - 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/48 - 1/52 - 1/54=1,

a(33)=730,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 + 1/10 - 1/11 - 1/12 - 1/13 - 1/14 - 1/15 + 1/16 + 1/18 + 1/20 - 1/21 - 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/48 - 1/52 - 1/54=1,

a(34)=774,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 - 1/8 + 1/9 - 1/10 + 1/11 + 1/12 - 1/13 - 1/14 + 1/15 + 1/16 + 1/18 - 1/20 - 1/21 + 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/48 - 1/52 - 1/54=1,

a(35)=819,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 - 1/8 + 1/9 + 1/10 + 1/11 - 1/12 - 1/13 - 1/14 + 1/15 + 1/16 - 1/18 + 1/20 - 1/21 + 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54=1,

a(36)=874,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 - 1/10 - 1/11 + 1/12 - 1/13 - 1/14 + 1/15 + 1/16 - 1/18 - 1/20 - 1/21 + 1/22 + 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55=1,

a(37)=930,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 - 1/10 - 1/11 + 1/12 - 1/13 + 1/14 + 1/15 - 1/16 - 1/18 - 1/20 - 1/21 + 1/22 + 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56=1,

a(38)=990,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 - 1/10 - 1/11 + 1/12 - 1/13 + 1/14 + 1/15 - 1/16 - 1/18 + 1/20 - 1/21 + 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60=1,

a(39)=1053,1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 - 1/9 - 1/10 - 1/11 + 1/12 - 1/13 - 1/14 + 1/15 - 1/16 - 1/18 + 1/20 + 1/21 + 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63=1,

a(40)=1118,1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 - 1/9 - 1/10 - 1/11 + 1/12 + 1/13 - 1/14 + 1/15 - 1/16 - 1/18 - 1/20 + 1/21 + 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 + 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65=1,

a(41)=1184,1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 - 1/9 - 1/10 + 1/11 - 1/12 + 1/13 - 1/14 + 1/15 - 1/16 - 1/18 - 1/20 + 1/21 + 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 + 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66=1,

a(42)=1254,1/2 + 1/3 + 1/4 - 1/5 + 1/6 + 1/7 + 1/8 - 1/9 + 1/10 + 1/11 + 1/12 + 1/13 + 1/14 + 1/15 - 1/16 - 1/18 - 1/20 - 1/21 + 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 + 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70=1,

a(43)=1326,1/2 + 1/3 + 1/4 - 1/5 + 1/6 + 1/7 + 1/8 + 1/9 - 1/10 + 1/11 + 1/12 + 1/13 + 1/14 - 1/15 + 1/16 - 1/18 - 1/20 - 1/21 + 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 + 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72=1,

a(44)=1403,1/2 + 1/3 + 1/4 - 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 - 1/11 + 1/12 + 1/13 - 1/14 + 1/15 + 1/16 - 1/18 - 1/20 + 1/21 - 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 + 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77=1,

a(45)=1481,1/2 + 1/3 + 1/4 - 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 - 1/11 + 1/12 + 1/13 - 1/14 + 1/15 + 1/16 - 1/18 - 1/20 + 1/21 - 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78=1,

a(46)=1565,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 - 1/8 + 1/9 + 1/10 - 1/11 + 1/12 + 1/13 + 1/14 + 1/15 + 1/16 - 1/18 + 1/20 - 1/21 - 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84=1,

a(47)=1653,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 - 1/8 + 1/9 + 1/10 - 1/11 + 1/12 + 1/13 + 1/14 + 1/15 - 1/16 - 1/18 + 1/20 - 1/21 + 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 + 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88=1,

a(48)=1743,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 - 1/8 + 1/9 + 1/10 - 1/11 + 1/12 + 1/13 + 1/14 + 1/15 - 1/16 + 1/18 - 1/20 - 1/21 + 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 + 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90=1,

a(49)=1842,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 + 1/10 - 1/11 - 1/12 + 1/13 + 1/14 + 1/15 - 1/16 - 1/18 - 1/20 - 1/21 + 1/22 + 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/99=1,

a(50)=1946,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 + 1/10 - 1/11 - 1/12 - 1/13 + 1/14 + 1/15 + 1/16 - 1/18 - 1/20 - 1/21 + 1/22 + 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 + 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/99 - 1/104=1,

a(51)=2051,1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 - 1/11 - 1/12 - 1/13 - 1/14 - 1/15 + 1/16 - 1/18 - 1/20 - 1/21 + 1/22 + 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 + 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/99 - 1/104 - 1/105=1,]\[LongDash]\[LongDash]2051,

a(52)=2159,Z[1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 - 1/9 + 1/10 - 1/11 + 1/12 - 1/13 - 1/14 - 1/15 + 1/16 + 1/18 - 1/20 - 1/21 + 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 + 1/52 + 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/99 - 1/104 - 1/105 - 1/108=1,]\[LongDash]\[LongDash]2159,

a(53)=2269,Z[1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 - 1/9 + 1/10 - 1/11 + 1/12 - 1/13 - 1/14 - 1/15 + 1/16 + 1/18 + 1/20 - 1/21 - 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 + 1/52 + 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110=1,]\[LongDash]\[LongDash]2269,

a(54)=2386,Z[1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 - 1/10 - 1/11 + 1/12 + 1/13 - 1/14 + 1/15 + 1/16 - 1/18 - 1/20 - 1/21 - 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 + 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117=1,]\[LongDash]\[LongDash]2386,

a(55)=2506,Z[1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 - 1/11 - 1/12 + 1/13 - 1/14 + 1/15 - 1/16 - 1/18 + 1/20 - 1/21 - 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 + 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117 - 1/120=1,]\[LongDash]\[LongDash]2506,

a(56)=2632,Z[1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 - 1/9 + 1/10 - 1/11 + 1/12 + 1/13 + 1/14 + 1/15 - 1/16 + 1/18 + 1/20 + 1/21 - 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 + 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117 - 1/120 - 1/126=1,]\[LongDash]\[LongDash]2632,

a(57)=2762,Z[1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 - 1/9 - 1/10 + 1/11 + 1/12 - 1/13 + 1/14 + 1/15 - 1/16 + 1/18 - 1/20 + 1/21 + 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 + 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 + 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117 - 1/120 - 1/126 - 1/130=1,]\[LongDash]\[LongDash]2762,

a(58)=2894,Z[1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 - 1/9 + 1/10 - 1/11 + 1/12 - 1/13 + 1/14 - 1/15 - 1/16 + 1/18 + 1/20 + 1/21 + 1/22 + 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 + 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117 - 1/120 - 1/126 - 1/130 - 1/132=1,]\[LongDash]\[LongDash]2894,

a(59)=3029,Z[1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 - 1/10 - 1/11 + 1/12 - 1/13 + 1/14 + 1/15 - 1/16 - 1/18 + 1/20 + 1/21 + 1/22 + 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117 - 1/120 - 1/126 - 1/130 - 1/132 - 1/135=1,]\[LongDash]\[LongDash]3029,

a(60)=3169,Z[1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 - 1/10 - 1/11 + 1/12 - 1/13 + 1/14 + 1/15 - 1/16 - 1/18 - 1/20 - 1/21 + 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117 - 1/120 - 1/126 - 1/130 - 1/132 - 1/135 - 1/140=1,]\[LongDash]\[LongDash]3169,

光滑数(13)——A080197——{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 35, 36, 39, 40, 42, 44, 45, 48, 49, 50, 52, 54, 55, 56, 60, 63, 64, 65, 66, 70, 72, 75, 77, 78, 80,
81, 84, 88, 90, 91, 96, 98, 99, 100, 104, 105, 108, 110, 112, 117, 120, 121, 125, 126, 128, 130, 132, 135, 140, 143, 144, 147, 150, 154, 156, 160, 162, 165, 168, 169, 175, 176, 180, 182, 189, 192, 195, 196, 198, 200,

  1. 光滑数(13)——其质因数都小于等于13的数字。Select[Range[300], Max[FactorInteger[#][[All, 1]]] <= 13 &]
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王守恩
 楼主| 发表于 2026-2-7 10:53:07 | 显示全部楼层
简单的——先搞。 满足 n 项倒数和(允许 "+" 或 "-" ) = 1。a(n) = n 项和不是最小的。——满足：无限数字串！

a(03)=11, 1/2 + 1/3 + 1/6=1,

a(04)=21, 1/2 + 1/3 + 1/4 - 1/12=1,

a(05)=27, 1/2 + 1/3 + 1/4 - 1/6 + 1/12=1,

a(06)=40, 1/2 + 1/3 + 1/4 - 1/5 + 1/6 - 1/20=1,

a(07)=50, 1/2 + 1/3 + 1/4 - 1/5 + 1/6 - 1/10 + 1/20=1,

a(08)=57, 1/2 + 1/3 - 1/4 + 1/5 + 1/6 - 1/10 + 1/12 + 1/15=1,

a(09)=77, 1/2 + 1/3 - 1/4 + 1/5 + 1/6 + 1/8 - 1/10 + 1/15 - 1/24=1,

a(10)=84, 1/2 - 1/3 + 1/4 + 1/5 + 1/6 + 1/9 - 1/10 + 1/12 + 1/15 + 1/18=1,

a(11)=99,  1/2 - 1/3 + 1/4 + 1/5 + 1/6 + 1/7 - 1/10 + 1/12 + 1/14 + 1/15 - 1/21=1,

a(12)=116, 1/2 - 1/3 + 1/4 + 1/5 + 1/6 + 1/8 + 1/9 - 1/10 - 1/12 + 1/15 + 1/18 + 1/24=1,

a(13)=126, 1/2 + 1/3 - 1/4 + 1/5 + 1/6 - 1/7 + 1/9 - 1/10 + 1/12 - 1/14 + 1/15 + 1/18 + 1/21=1,

a(14)=146, 1/2 - 1/3 + 1/4 + 1/5 + 1/6 + 1/7 - 1/8 + 1/9 - 1/10 + 1/14 + 1/15 + 1/18 - 1/21 + 1/24=1,

a(15)=158, 1/2 - 1/3 + 1/4 + 1/5 - 1/6 + 1/7 + 1/8 + 1/9 - 1/10 + 1/12 + 1/14 + 1/15 + 1/18 - 1/21 + 1/24=1,

a(16)=178, 1/2 - 1/3 + 1/4 + 1/5 - 1/6 + 1/7 - 1/8 + 1/9 + 1/10 + 1/12 + 1/14 + 1/15 + 1/18 + 1/20 - 1/21 + 1/24=1,

a(17)=196, 1/2 - 1/3 + 1/4 + 1/5 - 1/6 - 1/7 + 1/8 + 1/9 + 1/10 + 1/12 + 1/14 + 1/15 + 1/18 + 1/20 - 1/21 + 1/24 + 1/28=1,

a(18)=224, 1/2 - 1/3 + 1/4 + 1/5 - 1/6 + 1/7 + 1/8 + 1/9 - 1/10 + 1/11 - 1/12 + 1/14 + 1/15 + 1/18 - 1/21 + 1/22 + 1/24 + 1/33=1,

a(19)=244, 1/2 + 1/3 - 1/4 + 1/5 - 1/6 - 1/7 + 1/8 + 1/9 + 1/10 + 1/11 - 1/12 - 1/14 + 1/15 + 1/18 + 1/20 + 1/21 + 1/22 - 1/24 + 1/33=1,

a(20)=272, 1/2 - 1/3 - 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 + 1/10 + 1/11 + 1/12 + 1/14 + 1/15 + 1/18 + 1/20 - 1/21 + 1/22 + 1/24 + 1/28 + 1/33=1,

a(21)=302, 1/2 - 1/3 + 1/4 + 1/5 - 1/6 - 1/7 + 1/8 + 1/9 - 1/10 + 1/11 + 1/12 + 1/14 + 1/15 + 1/18 + 1/20 - 1/21 + 1/22 + 1/24 + 1/28 + 1/30 + 1/33=1,

a(22)=336, 1/2 - 1/3 + 1/4 + 1/5 - 1/6 - 1/7 - 1/8 + 1/9 + 1/10 + 1/11 + 1/12 + 1/14 + 1/15 + 1/16 + 1/18 + 1/20 - 1/21 + 1/22 + 1/24 + 1/28 + 1/33 + 1/48=1,

a(23)=366, 1/2 + 1/3 - 1/4 - 1/5 + 1/6 + 1/7 - 1/8 + 1/9 - 1/10 + 1/11 + 1/12 - 1/14 + 1/15 + 1/16 + 1/18 - 1/20 + 1/21 + 1/22 + 1/24 - 1/28 + 1/30 + 1/33 + 1/48=1,

a(24)=401, 1/2 + 1/3 - 1/4 - 1/5 + 1/6 - 1/7 - 1/8 + 1/9 - 1/10 + 1/11 + 1/12 + 1/14 + 1/15 + 1/16 + 1/18 + 1/20 + 1/21 + 1/22 + 1/24 + 1/28 + 1/30 + 1/33 - 1/35 + 1/48=1,

a(25)=437, 1/2 - 1/3 + 1/4 - 1/5 - 1/6 + 1/7 + 1/8 + 1/9 + 1/10 + 1/11 + 1/12 - 1/14 + 1/15 + 1/16 - 1/18 + 1/20 + 1/21 + 1/22 + 1/24 + 1/28 - 1/30 + 1/33 + 1/35 + 1/36 + 1/48=1,

a(26)=477, 1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 - 1/8 - 1/9 + 1/10 - 1/11 + 1/12 + 1/14 - 1/15 + 1/16 + 1/18 + 1/20 - 1/21 - 1/22 - 1/24 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/40 - 1/48=1,

a(27)=518, 1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 - 1/8 + 1/9 - 1/10 - 1/11 + 1/12 + 1/14 + 1/15 - 1/16 + 1/18 + 1/20 - 1/21 - 1/22 - 1/24 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/48 - 1/54=1,

a(28)=531, 1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 - 1/8 + 1/9 - 1/10 - 1/11 + 1/12 - 1/13 + 1/14 + 1/15 - 1/16 + 1/18 + 1/20 - 1/21 - 1/22 - 1/24 + 1/26 - 1/28 - 1/30 - 1/33 - 1/35 - 1/39 - 1/48 - 1/52=1,

a(29)=567, 1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 - 1/9 - 1/10 - 1/11 + 1/12 - 1/13 + 1/14 + 1/15 - 1/16 + 1/18 + 1/20 - 1/21 - 1/22 - 1/24 + 1/26 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/48 - 1/52=1,

a(30)=607,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 - 1/9 - 1/10 - 1/11 + 1/12 - 1/13 + 1/14 + 1/15 + 1/16 + 1/18 - 1/20 - 1/21 - 1/22 - 1/24 + 1/26 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/48 - 1/52=1,

a(31)=648,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 - 1/10 - 1/11 - 1/12 - 1/13 + 1/14 + 1/15 - 1/16 + 1/18 + 1/20 - 1/21 - 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/48 - 1/52 - 1/54=1,

a(32)=688,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 - 1/10 - 1/11 - 1/12 - 1/13 + 1/14 + 1/15 + 1/16 + 1/18 - 1/20 - 1/21 - 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/48 - 1/52 - 1/54=1,

a(33)=730,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 + 1/10 - 1/11 - 1/12 - 1/13 - 1/14 - 1/15 + 1/16 + 1/18 + 1/20 - 1/21 - 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/48 - 1/52 - 1/54=1,

a(34)=774,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 - 1/8 + 1/9 - 1/10 + 1/11 + 1/12 - 1/13 - 1/14 + 1/15 + 1/16 + 1/18 - 1/20 - 1/21 + 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/48 - 1/52 - 1/54=1,

a(35)=819,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 - 1/8 + 1/9 + 1/10 + 1/11 - 1/12 - 1/13 - 1/14 + 1/15 + 1/16 - 1/18 + 1/20 - 1/21 + 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54=1,

a(36)=874,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 - 1/10 - 1/11 + 1/12 - 1/13 - 1/14 + 1/15 + 1/16 - 1/18 - 1/20 - 1/21 + 1/22 + 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55=1,

a(37)=930,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 - 1/10 - 1/11 + 1/12 - 1/13 + 1/14 + 1/15 - 1/16 - 1/18 - 1/20 - 1/21 + 1/22 + 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56=1,

a(38)=990,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 - 1/10 - 1/11 + 1/12 - 1/13 + 1/14 + 1/15 - 1/16 - 1/18 + 1/20 - 1/21 + 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60=1,

a(39)=1053,1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 - 1/9 - 1/10 - 1/11 + 1/12 - 1/13 - 1/14 + 1/15 - 1/16 - 1/18 + 1/20 + 1/21 + 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63=1,

a(40)=1118,1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 - 1/9 - 1/10 - 1/11 + 1/12 + 1/13 - 1/14 + 1/15 - 1/16 - 1/18 - 1/20 + 1/21 + 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 + 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65=1,

a(41)=1184,1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 - 1/9 - 1/10 + 1/11 - 1/12 + 1/13 - 1/14 + 1/15 - 1/16 - 1/18 - 1/20 + 1/21 + 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 + 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66=1,

a(42)=1254,1/2 + 1/3 + 1/4 - 1/5 + 1/6 + 1/7 + 1/8 - 1/9 + 1/10 + 1/11 + 1/12 + 1/13 + 1/14 + 1/15 - 1/16 - 1/18 - 1/20 - 1/21 + 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 + 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70=1,

a(43)=1326,1/2 + 1/3 + 1/4 - 1/5 + 1/6 + 1/7 + 1/8 + 1/9 - 1/10 + 1/11 + 1/12 + 1/13 + 1/14 - 1/15 + 1/16 - 1/18 - 1/20 - 1/21 + 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 + 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72=1,

a(44)=1403,1/2 + 1/3 + 1/4 - 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 - 1/11 + 1/12 + 1/13 - 1/14 + 1/15 + 1/16 - 1/18 - 1/20 + 1/21 - 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 + 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77=1,

a(45)=1481,1/2 + 1/3 + 1/4 - 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 - 1/11 + 1/12 + 1/13 - 1/14 + 1/15 + 1/16 - 1/18 - 1/20 + 1/21 - 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78=1,

a(46)=1565,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 - 1/8 + 1/9 + 1/10 - 1/11 + 1/12 + 1/13 + 1/14 + 1/15 + 1/16 - 1/18 + 1/20 - 1/21 - 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84=1,

a(47)=1653,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 - 1/8 + 1/9 + 1/10 - 1/11 + 1/12 + 1/13 + 1/14 + 1/15 - 1/16 - 1/18 + 1/20 - 1/21 + 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 + 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88=1,

a(48)=1743,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 - 1/8 + 1/9 + 1/10 - 1/11 + 1/12 + 1/13 + 1/14 + 1/15 - 1/16 + 1/18 - 1/20 - 1/21 + 1/22 - 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 + 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90=1,

a(49)=1834,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 + 1/10 - 1/11 - 1/12 + 1/13 - 1/14 + 1/15 - 1/16 + 1/18 - 1/20 - 1/21 + 1/22 + 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 + 1/44 - 1/45 - 1/48 + 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91=1,]\[LongDash]\[LongDash]1834,

a(50)=1933,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 + 1/10 - 1/11 + 1/12 + 1/13 - 1/14 + 1/15 - 1/16 - 1/18 - 1/20 - 1/21 + 1/22 + 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 + 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91 - 1/99=1,]\[LongDash]\[LongDash]1933,

a(51)=2037,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 + 1/10 - 1/11 + 1/12 - 1/13 - 1/14 + 1/15 + 1/16 - 1/18 - 1/20 - 1/21 + 1/22 + 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91 - 1/99 - 1/104=1,]\[LongDash]\[LongDash]2037,

a(52)=2142,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 + 1/10 - 1/11 + 1/12 - 1/13 + 1/14 - 1/15 + 1/16 - 1/18 - 1/20 - 1/21 + 1/22 + 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91 - 1/99 - 1/104 - 1/105=1,]\[LongDash]\[LongDash]2142,

a(53)=2250,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 - 1/9 + 1/10 - 1/11 + 1/12 - 1/13 + 1/14 - 1/15 + 1/16 + 1/18 - 1/20 + 1/21 + 1/22 - 1/24 + 1/26 - 1/27 + 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 + 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91 - 1/99 - 1/104 - 1/105 - 1/108=1,]\[LongDash]\[LongDash]2250,

a(54)=2360,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 - 1/9 + 1/10 - 1/11 + 1/12 - 1/13 + 1/14 - 1/15 + 1/16 + 1/18 + 1/20 + 1/21 - 1/22 - 1/24 + 1/26 - 1/27 + 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 + 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110=1,]\[LongDash]\[LongDash]2360,

a(55)=2477,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 + 1/10 - 1/11 + 1/12 - 1/13 + 1/14 + 1/15 + 1/16 - 1/18 - 1/20 - 1/21 - 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 + 1/54 - 1/55 - 1/56 - 1/60 - 1/63 + 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117=1,]\[LongDash]\[LongDash]2477,

a(56)=2597,1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 + 1/10 - 1/11 + 1/12 - 1/13 + 1/14 - 1/15 - 1/16 - 1/18 + 1/20 + 1/21 - 1/22 - 1/24 + 1/26 - 1/27 + 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 + 1/54 - 1/55 - 1/56 - 1/60 - 1/63 + 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117 - 1/120=1,]\[LongDash]\[LongDash]2597,

a(57)=2723,1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 - 1/9 + 1/10 - 1/11 + 1/12 - 1/13 + 1/14 - 1/15 - 1/16 + 1/18 + 1/20 - 1/21 - 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 + 1/54 - 1/55 - 1/56 - 1/60 - 1/63 + 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117 - 1/120 - 1/126=1,]\[LongDash]\[LongDash]2723,

a(58)=2853,1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 - 1/9 - 1/10 - 1/11 + 1/12 + 1/13 + 1/14 + 1/15 - 1/16 + 1/18 - 1/20 - 1/21 - 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 + 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117 - 1/120 - 1/126 - 1/130=1,]\[LongDash]\[LongDash]2853,

a(59)=2985,1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 - 1/8 - 1/9 + 1/10 - 1/11 + 1/12 + 1/13 + 1/14 - 1/15 - 1/16 + 1/18 + 1/20 - 1/21 + 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 + 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117 - 1/120 - 1/126 - 1/130 - 1/132=1,]\[LongDash]\[LongDash]2985,

a(60)=3120,Z[1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 - 1/8 + 1/9 - 1/10 - 1/11 + 1/12 + 1/13 + 1/14 + 1/15 - 1/16 - 1/18 + 1/20 - 1/21 + 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117 - 1/120 - 1/126 - 1/130 - 1/132 - 1/135=1,]\[LongDash]\[LongDash]3120,

a(61)=3260,Z[1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 - 1/10 - 1/11 + 1/12 + 1/13 - 1/14 + 1/15 - 1/16 - 1/18 - 1/20 - 1/21 + 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117 - 1/120 - 1/126 - 1/130 - 1/132 - 1/135 - 1/140=1,]\[LongDash]\[LongDash]3260,

a(62)=3403,Z[1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 - 1/11 + 1/12 - 1/13 - 1/14 - 1/15 - 1/16 - 1/18 + 1/20 - 1/21 + 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 + 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117 - 1/120 - 1/126 - 1/130 - 1/132 - 1/135 - 1/140 - 1/143=1,]\[LongDash]\[LongDash]3403,

a(63)=3557,Z[1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 - 1/11 + 1/12 - 1/13 + 1/14 - 1/15 - 1/16 - 1/18 + 1/20 - 1/21 - 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117 - 1/120 - 1/126 - 1/130 - 1/132 - 1/135 - 1/140 - 1/143 - 1/154=1,]\[LongDash]\[LongDash]3557,

a(64)=3713,Z[1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 - 1/11 + 1/12 - 1/13 + 1/14 - 1/15 - 1/16 - 1/18 + 1/20 - 1/21 - 1/22 + 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117 - 1/120 - 1/126 - 1/130 - 1/132 - 1/135 - 1/140 - 1/143 - 1/154 - 1/156=1,]\[LongDash]\[LongDash]3713,

a(65)=3878,Z[1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 + 1/11 - 1/12 - 1/13 + 1/14 - 1/15 - 1/16 - 1/18 - 1/20 - 1/21 + 1/22 + 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117 - 1/120 - 1/126 - 1/130 - 1/132 - 1/135 - 1/140 - 1/143 - 1/154 - 1/156 - 1/165=1,]\[LongDash]\[LongDash]3878,

a(66)=4046,Z[1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 + 1/9 + 1/10 + 1/11 + 1/12 - 1/13 + 1/14 - 1/15 + 1/16 - 1/18 - 1/20 - 1/21 + 1/22 + 1/24 - 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117 - 1/120 - 1/126 - 1/130 - 1/132 - 1/135 - 1/140 - 1/143 - 1/154 - 1/156 - 1/165 - 1/168=1,]\[LongDash]\[LongDash]4046,

a(67)=4226,Z[1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 - 1/9 - 1/10 + 1/11 + 1/12 - 1/13 + 1/14 + 1/15 + 1/16 + 1/18 + 1/20 + 1/21 + 1/22 - 1/24 - 1/26 - 1/27 + 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117 - 1/120 - 1/126 - 1/130 - 1/132 - 1/135 - 1/140 - 1/143 - 1/154 - 1/156 - 1/165 - 1/168 - 1/180=1,]\[LongDash]\[LongDash]4226,

a(68)=4408,Z[1/2 + 1/3 + 1/4 + 1/5 + 1/6 - 1/7 + 1/8 - 1/9 - 1/10 + 1/11 + 1/12 - 1/13 + 1/14 + 1/15 + 1/16 + 1/18 + 1/20 + 1/21 + 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 - 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117 - 1/120 - 1/126 - 1/130 - 1/132 - 1/135 - 1/140 - 1/143 - 1/154 - 1/156 - 1/165 - 1/168 - 1/180 - 1/182=1,]\[LongDash]\[LongDash]4408,

a(69)=4597,Z[1/2 + 1/3 + 1/4 - 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 + 1/11 + 1/12 - 1/13 + 1/14 - 1/15 + 1/16 - 1/18 + 1/20 - 1/21 + 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 - 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 + 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117 - 1/120 - 1/126 - 1/130 - 1/132 - 1/135 - 1/140 - 1/143 - 1/154 - 1/156 - 1/165 - 1/168 - 1/180 - 1/182 - 1/189=1,]\[LongDash]\[LongDash]4597,

a(70)=4792,Z[1/2 + 1/3 + 1/4 + 1/5 - 1/6 + 1/7 + 1/8 + 1/9 + 1/10 + 1/11 - 1/12 + 1/13 + 1/14 - 1/15 + 1/16 - 1/18 - 1/20 - 1/21 + 1/22 - 1/24 + 1/26 - 1/27 - 1/28 - 1/30 - 1/33 - 1/35 - 1/36 + 1/39 - 1/40 - 1/42 - 1/44 - 1/45 - 1/48 - 1/52 + 1/54 - 1/55 - 1/56 - 1/60 - 1/63 - 1/65 - 1/66 - 1/70 - 1/72 - 1/77 - 1/78 - 1/84 - 1/88 - 1/90 - 1/91 - 1/99 - 1/104 - 1/105 - 1/108 - 1/110 - 1/117 - 1/120 - 1/126 - 1/130 - 1/132 - 1/135 - 1/140 - 1/143 - 1/154 - 1/156 - 1/165 - 1/168 - 1/180 - 1/182 - 1/189 - 1/195=1,]\[LongDash]\[LongDash]4792，

a(71)=4990{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198}

a(72)=5200{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210}

a(73)=5416{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216}

a(74)=5636{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220}

a(75)=5867{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231}

a(76)=6101{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234}

a(77)=6353{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252}

a(78)=6613{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260}

a(79)=6877{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,}

a(80)=7147{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270}

a(81)=7420{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273}

a(82)=7700{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280}

a(83)=7986{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286}

a(84)=8283{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297}

a(85)=8591{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297,308}

a(86)=8903{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297,308,312}

a(87)=9218{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297,308,312,315}

a(88)=9548{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297,308,312,315,330}

a(89)=9899{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297,308,312,315,330,351}

a(90)=10259{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297,308,312,315,330,351,360}

a(91)=10623{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297,308,312,315,330,351,360,364}

a(92)=11001{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297,308,312,315,330,351,360,364,378}

a(93)=11386{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297,308,312,315,330,351,360,364,378,385}

a(94)=11776{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297,308,312,315,330,351,360,364,378,385,390}

a(95)=12172{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297,308,312,315,330,351,360,364,378,385,390,396}

a(96)=12592{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297,308,312,315,330,351,360,364,378,385,390,396,420}

a(97)=13021{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297,308,312,315,330,351,360,364,378,385,390,396,420,429}

a(98)=13461{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297,308,312,315,330,351,360,364,378,385,390,396,420,429,440}

a(99)=13916{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297,308,312,315,330,351,360,364,378,385,390,396,420,429,440,455}

a(100)=14378{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297,308,312,315,330,351,360,364,378,385,390,396,420,429,440,455,462}

a(100)符号分配: {14378,"+"= {2, 3, 4, 5, 6, 8, 10, 12, 13, 14, 16, 18, 20, 21, 22, 26, 28}, "-"={7, 9, 11, 15, 24, 27, 30, 33, 35, 36, 39, 40, 42, 44, 45, 48, 52, 54, 55, 56, 60, 63, 65, 66, 70, 72, 77, 78, 84, 88, 90, 91,  99, 104, 105, 108,
110, 117, 120, 126, 130, 132, 135, 140, 143, 154, 156, 165, 168, 180, 182, 189, 195, 198, 210, 216, 220, 231, 234, 252, 260, 264, 270, 273, 280, 286, 297, 308, 312, 315, 330, 351, 360, 364, 378, 385, 390, 396, 420, 429, 440, 455, 462}}

前100项: {2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297,308,312,315,330,351,360,364,378,385,390,396,420,429,440,455,462}

前100个累加和: {2,5,9,14,20,27,35,44,54,65,77,90,104,119,135,153,173,194,216,240,266,293,321,351,384,419,455,494,534,576,620,665,713,765,819,874,930,990,1053,1118,1184,1254,1326,1403,1481,1565,1653,1743,1834,1933,2037,2142,2250,2360,2477,2597,2723,2853,2985,3120,3260,3403,3557,3713,3878,4046,4226,4408,4597,4792,4990,5200,5416,5636,5867,6101,6353,6613,6877,7147,7420,7700,7986,8283,8591,8903,9218,9548,9899,10259,10623,11001,11386,11776,12172,12592,13021,13461,13916,14378}
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王守恩
 楼主| 发表于 2026-2-7 18:00:55 | 显示全部楼层
前200项: {2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297,308,312,315,330,351,360,364,378,385,390,396,420,429,440,455,462,468,495,504,520,540,546,572,585,594,616,630,660,693,702,715,728,756,770,780,792,819,840,858,910,924,936,945,990,1001,1080,1092,1144,1155,1170,1188,1260,1287,1320,1365,1386,1404,1430,1485,1512,1540,1560,1638,1716,1755,1820,1848,1890,1980,2002,2079,2145,2184,2310,2340,2376,2457,2520,2574,2730,2772,2808,2860,2970,3003,3080,3276,3432,3465,3510,3640,3780,3861,3960,4004,4095,4158,4290,4620,4680,4914,5005,5148,5460,5544,5720,5940,6006,6435,6552,6930,7020,7560,7722,8008,8190}

前200个累加和: {2,5,9,14,20,27,35,44,54,65,77,90,104,119,135,153,173,194,216,240,266,293,321,351,384,419,455,494,534,576,620,665,713,765,819,874,930,990,1053,1118,1184,1254,1326,1403,1481,1565,1653,1743,1834,1933,2037,2142,2250,2360,2477,2597,2723,2853,2985,3120,3260,3403,3557,3713,3878,4046,4226,4408,4597,4792,4990,5200,5416,5636,5867,6101,6353,6613,6877,7147,7420,7700,7986,8283,8591,8903,9218,9548,9899,10259,10623,11001,11386,11776,12172,12592,13021,13461,13916,14378,14846,15341,15845,16365,16905,17451,18023,18608,19202,19818,20448,21108,21801,22503,23218,23946,24702,25472,26252,27044,27863,28703,29561,30471,31395,32331,33276,34266,35267,36347,37439,38583,39738,40908,42096,43356,44643,45963,47328,48714,50118,51548,53033,54545,56085,57645,59283,60999,62754,64574,66422,68312,70292,72294,74373,76518,78702,81012,83352,85728,88185,90705,93279,96009,98781,101589,104449,107419,110422,113502,116778,120210,123675,127185,130825,134605,138466,142426,146430,150525,154683,158973,163593,168273,173187,178192,183340,188800,194344,200064,206004,212010,218445,224997,231927,238947,246507,254229,262237,270427}

a(200)=270427{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297,308,312,315,330,351,360,364,378,385,390,396,420,429,440,455,462,468,495,504,520,540,546,572,585,594,616,630,660,693,702,715,728,756,770,780,792,819,840,858,910,924,936,945,990,1001,1080,1092,1144,1155,1170,1188,1260,1287,1320,1365,1386,1404,1430,1485,1512,1540,1560,1638,1716,1755,1820,1848,1890,1980,2002,2079,2145,2184,2310,2340,2376,2457,2520,2574,2730,2772,2808,2860,2970,3003,3080,3276,3432,3465,3510,3640,3780,3861,3960,4004,4095,4158,4290,4620,4680,4914,5005,5148,5460,5544,5720,5940,6006,6435,6552,6930,7020,7560,7722,8008,8190}

a(200)符号分配: {270427,"+"={2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 18, 20, 21, 22, 24, 33}, "-"={7, 11, 13, 16, 26, 27, 28, 30, 35, 36, 39, 40, 42, 44, 45, 48, 52, 54, 55, 56, 60, 63, 65, 66, 70, 72, 77, 78, 84, 88, 90, 91, 99, 104, 105,
108, 110, 117, 120, 126, 130, 132, 135, 140, 143, 154, 156, 165, 168, 180, 182, 189, 195, 198, 210, 216, 220, 231, 234, 252, 260, 264, 270, 273, 280, 286, 297, 308, 312, 315, 330, 351, 360, 364, 378, 385, 390, 396, 420, 429, 440,
455, 462, 468, 495, 504, 520, 540, 546, 572, 585, 594, 616, 630, 660, 693, 702, 715, 728, 756, 770, 780, 792, 819, 840, 858, 910, 924, 936, 945, 990, 1001, 1080, 1092, 1144, 1155, 1170, 1188, 1260, 1287, 1320, 1365, 1386, 1404,
1430, 1485, 1512, 1540, 1560, 1638, 1716, 1755, 1820, 1848, 1890, 1980, 2002, 2079, 2145, 2184, 2310, 2340, 2376, 2457, 2520, 2574, 2730, 2772, 2808, 2860, 2970, 3003, 3080, 3276, 3432, 3465, 3510, 3640, 3780, 3861, 3960,
4004, 4095, 4158, 4290, 4620, 4680, 4914, 5005, 5148, 5460, 5544, 5720, 5940, 6006, 6435, 6552, 6930, 7020, 7560, 7722, 8008, 8190}}

2个代码。
  1. s = {16, 25, 49, 81, 121, 169}; A = Select[Select[Range[2, 20000], Max[FactorInteger[#][[All, 1]]] <= 13 &], Function[n, Module[{k = True, q}, Do[q = s[[i]];
  2. If[Mod[n, q] == 0,  If[q == 16, If[! (n == 16 || n == 48), k = False];, k = False;]; Break[];];, {i, Length[s]}]; k]]]; A = Sort[A]; B = Accumulate[A];
  3. Print["序列长度: ", Length[A]]
  4. Print["前100项: ", Take[A, 200]]
  5. Print["前20个累加和: ", Take[B, 200]]
复制代码

符号分配: 用的是这个代码。
  1. d = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 33, 35, 36, 39, 40, 42, 44, 45, 48, 52, 54, 55, 56, 60, 63, 65, 66, 70, 72, 77, 78,
  2. 84, 88, 90, 91, 99, 104, 105, 108, 110, 117, 120, 126, 130, 132, 135, 140, 143, 154, 156, 165, 168, 180, 182, 189, 195, 198, 210, 216, 220, 231, 234, 252, 260, 264, 270, 273,
  3. 280, 286, 297, 308, 312, 315, 330, 351, 360, 364, 378, 385, 390, 396, 420, 429, 440, 455, 462, 468, 495, 504, 520, 540, 546, 572, 585, 594, 616, 630, 660, 693, 702, 715, 728,
  4. 756, 770, 780, 792, 819, 840, 858, 910, 924, 936, 945, 990, 1001, 1080, 1092, 1144, 1155, 1170, 1188, 1260, 1287, 1320, 1365, 1386, 1404, 1430, 1485, 1512, 1540, 1560, 1638,
  5. 1716, 1755, 1820, 1848, 1890, 1980, 2002, 2079, 2145, 2184, 2310, 2340, 2376, 2457, 2520, 2574, 2730, 2772, 2808, 2860, 2970, 3003, 3080, 3276, 3432, 3465, 3510, 3640, 3780,
  6. 3861, 3960, 4004, 4095, 4158, 4290, 4620, 4680, 4914, 5005, 5148, 5460, 5544, 5720, 5940, 6006, 6435, 6552, 6930, 7020, 7560, 7722, 8008, 8190};
  7. l = LCM @[url=home.php?mod=space&uid=6175]@[/url] d; u = l/d; T = Total[u]; g = (T + l)/2; R = Association[0 -> {}];
  8. Do[Do[If[KeyExistsQ[R, s], If[! KeyExistsQ[R, s + x], R[s + x] = Append[R[s], x]]], {s, Keys[R]}], {x, u}]; p = R[g]; V = Flatten[Position[u, #] & /@ p];
  9. B = d[[V]]; A = Complement[d, B]; r = Total[1/# & /@ B] - Total[1/# & /@ A]; {Total[d], r == 1, B, A}
复制代码

这是一个无限数字串。 满足 n 项倒数和(允许 "+" 或 "-" ) = 1。就这串数来说: a(n) = n 项和是最小的。——各位！！竞争一下——来个a(n)更小的！谢谢！！！
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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王守恩
 楼主| 发表于 2026-2-8 16:02:16 | 显示全部楼层
这串数是有限数字串——257项。

前257项:{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297,308,312,315,330,351,360,364,378,385,390,396,420,429,440,455,462,468,495,504,520,540,546,572,585,594,616,630,660,693,702,715,728,756,770,780,792,819,840,858,910,924,936,945,990,1001,1080,1092,1144,1155,1170,1188,1260,1287,1320,1365,1386,1404,1430,1485,1512,1540,1560,1638,1716,1755,1820,1848,1890,1980,2002,2079,2145,2184,2310,2340,2376,2457,2520,2574,2730,2772,2808,2860,2970,3003,3080,3276,3432,3465,3510,3640,3780,3861,3960,4004,4095,4158,4290,4620,4680,4914,5005,5148,5460,5544,5720,5940,6006,6435,6552,6930,7020,7560,7722,8008,8190,8316,8580,9009,9240,9828,10010,10296,10395,10920,11880,12012,12285,12870,13860,14040,15015,15444,16380,16632,17160,18018,19305,19656,20020,20790,24024,24570,25740,27027,27720,30030,30888,32760,36036,38610,40040,41580,45045,49140,51480,54054,60060,72072,77220,83160,90090,98280,108108,120120,135135,154440,180180,216216,270270,360360,540540,1081080}

前257个累加和:{2,5,9,14,20,27,35,44,54,65,77,90,104,119,135,153,173,194,216,240,266,293,321,351,384,419,455,494,534,576,620,665,713,765,819,874,930,990,1053,1118,1184,1254,1326,1403,1481,1565,1653,1743,1834,1933,2037,2142,2250,2360,2477,2597,2723,2853,2985,3120,3260,3403,3557,3713,3878,4046,4226,4408,4597,4792,4990,5200,5416,5636,5867,6101,6353,6613,6877,7147,7420,7700,7986,8283,8591,8903,9218,9548,9899,10259,10623,11001,11386,11776,12172,12592,13021,13461,13916,14378,14846,15341,15845,16365,16905,17451,18023,18608,19202,19818,20448,21108,21801,22503,23218,23946,24702,25472,26252,27044,27863,28703,29561,30471,31395,32331,33276,34266,35267,36347,37439,38583,39738,40908,42096,43356,44643,45963,47328,48714,50118,51548,53033,54545,56085,57645,59283,60999,62754,64574,66422,68312,70292,72294,74373,76518,78702,81012,83352,85728,88185,90705,93279,96009,98781,101589,104449,107419,110422,113502,116778,120210,123675,127185,130825,134605,138466,142426,146430,150525,154683,158973,163593,168273,173187,178192,183340,188800,194344,200064,206004,212010,218445,224997,231927,238947,246507,254229,262237,270427,278743,287323,296332,305572,315400,325410,335706,346101,357021,368901,380913,393198,406068,419928,433968,448983,464427,480807,497439,514599,532617,551922,571578,591598,612388,636412,660982,686722,713749,741469,771499,802387,835147,871183,909793,949833,991413,1036458,1085598,1137078,1191132,1251192,1323264,1400484,1483644,1573734,1672014,1780122,1900242,2035377,2189817,2369997,2586213,2856483,3216843,3757383,4838463}

a(257)=4838463{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,24,26,27,28,30,33,35,36,39,40,42,44,45,48,52,54,55,56,60,63,65,66,70,72,77,78,84,88,90,91,99,104,105,108,110,117,120,126,130,132,135,140,143,154,156,165,168,180,182,189,195,198,210,216,220,231,234,252,260,264,270,273,280,286,297,308,312,315,330,351,360,364,378,385,390,396,420,429,440,455,462,468,495,504,520,540,546,572,585,594,616,630,660,693,702,715,728,756,770,780,792,819,840,858,910,924,936,945,990,1001,1080,1092,1144,1155,1170,1188,1260,1287,1320,1365,1386,1404,1430,1485,1512,1540,1560,1638,1716,1755,1820,1848,1890,1980,2002,2079,2145,2184,2310,2340,2376,2457,2520,2574,2730,2772,2808,2860,2970,3003,3080,3276,3432,3465,3510,3640,3780,3861,3960,4004,4095,4158,4290,4620,4680,4914,5005,5148,5460,5544,5720,5940,6006,6435,6552,6930,7020,7560,7722,8008,8190,8316,8580,9009,9240,9828,10010,10296,10395,10920,11880,12012,12285,12870,13860,14040,15015,15444,16380,16632,17160,18018,19305,19656,20020,20790,24024,24570,25740,27027,27720,30030,30888,32760,36036,38610,40040,41580,45045,49140,51480,54054,60060,72072,77220,83160,90090,98280,108108,120120,135135,154440,180180,216216,270270,360360,540540,1081080}

a(257)符号分配:{4838463, "+"={2, 3, 4, 5, 6, 7, 8, 9, 10, 14, 15, 18, 20, 22, 28, 39}, "+"={11, 12, 13, 16, 21, 24, 26, 27, 30, 33, 35, 36, 40, 42, 44, 45, 48, 52, 54, 55, 56, 60, 63, 65, 66, 70, 72, 77, 78, 84, 88, 90, 91, 99, 104,
105, 108, 110, 117, 120, 126, 130, 132, 135, 140, 143, 154, 156, 165, 168, 180, 182, 189, 195, 198, 210, 216, 220, 231, 234, 252, 260, 264, 270, 273, 280, 286, 297, 308, 312, 315, 330, 351, 360, 364, 378, 385, 390, 396, 420,
429, 440, 455, 462, 468, 495, 504, 520, 540, 546, 572, 585, 594, 616, 630, 660, 693, 702, 715, 728, 756, 770, 780, 792, 819, 840, 858, 910, 924, 936, 945, 990, 1001, 1080, 1092, 1144, 1155, 1170, 1188, 1260, 1287, 1320, 1365,
1386, 1404, 1430, 1485, 1512, 1540, 1560, 1638, 1716, 1755, 1820, 1848, 1890, 1980, 2002, 2079, 2145, 2184, 2310, 2340, 2376, 2457, 2520, 2574, 2730, 2772, 2808, 2860, 2970, 3003, 3080, 3276, 3432, 3465, 3510, 3640, 3780,
3861, 3960, 4004, 4095, 4158, 4290, 4620, 4680, 4914, 5005, 5148, 5460, 5544, 5720, 5940, 6006, 6435, 6552, 6930, 7020, 7560, 7722, 8008, 8190, 8316, 8580, 9009, 9240, 9828, 10010, 10296, 10395, 10920, 11880, 12012, 12285,
12870, 13860, 14040, 15015, 15444, 16380, 16632, 17160, 18018, 19305, 19656, 20020, 20790, 24024, 24570, 25740, 27027, 27720, 30030, 30888, 32760, 36036, 38610, 40040, 41580, 45045, 49140, 51480, 54054, 60060, 72072,
77220, 83160, 90090, 98280, 108108, 120120, 135135, 154440, 180180, 216216, 270270, 360360, 540540, 1081080}}
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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王守恩
 楼主| 发表于 2026-2-10 10:30:35 | 显示全部楼层
方向明确：找一个数字串(有无限项), 满足 n 项倒数和(允许 "+" 或 "-" ) = 1。a(n) =  n 项最小和。

这个数字串——是有无限项, 也满足 n 项倒数和(允许 "+" 或 "-" ) = 1。只是 a(n) =  n 项和不是最小的。

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 49, 50, 54, 55, 56, 60, 63, 64, 66, 70, 72, 75, 77, 80, 81, 84, 88, 90, 96, 98, 99, 100, 105, 108, 110, 112,
120, 121, 125, 126, 128, 132, 135, 140, 144, 147, 150, 154, 160, 162, 165, 168, 175, 176, 180, 189, 192, 196, 198, 200, 210, 216, 220, 224, 225, 231, 240, 242, 243, 245, 250, 252, 256, 264, 270, 275, 280, 288, 294, 297,
300, 308, 315, 320, 324, 330, 336, 343, 350, 352, 360, 363, 375, 378, 384, 385, 392, 396, 400, 405, 420, 432, 440, 441, 448, 450, 462, 480, 484, 486, 490, 495, 500, 504, 512, 525, 528, 539, 540, 550, 560, 567, 576, 588,
594, 600, 605, 616, 625, 630, 640, 648, 660, 672, 675, 686, 693, 700, 704, 720, 726, 729, 735, 750, 756, 768, 770, 784, 792, 800, 810, 825, 840, 847, 864, 875, 880, 882, 891, 896, 900, 924, 945, 960, 968, 972, 980, 990}
  1. Select[Range[1000], Max[FactorInteger[#][[All, 1]]] <= 11 &]
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毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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王守恩
 楼主| 发表于 2026-2-10 18:25:49 | 显示全部楼层
方向明确：找一个数字串(有无限项), 满足 n 项倒数和(允许 "+" 或 "-" ) = 1。a(n) =  n 项最小和。

这个数字串可以有的——无限项, 满足 n 项倒数和(允许 "+" 或 "-" ) = 1。a(n) =  n 项最小和。——方法没问题——只是手工计算有误差。

a(03)={11, True, {2, 3, 6}, {}}

a(04)={12, True, {1, 2}, {3, 6}}

a(05)={22, True, {1, 3, 4}, {2, 12}}

a(06)={28, True, {1, 2, 6}, {3, 4, 12}}

a(07)={41, True, {1, 2, 4}, {3, 5, 6, 20}}

a(08)={51, True, {1, 2, 5, 10}, {3, 4, 6, 20}}

a(09)={58, True, {1, 2, 4, 10}, {3, 5, 6, 12, 15}}

a(10)={78, True, {1, 2, 6, 8, 10}, {3, 4, 5, 15, 24}}

a(11)={85, True, {1, 2, 3, 10}, {4, 5, 6, 9, 12, 15, 18}}

a(12)={100, True, {1, 2, 6, 7, 10, 14}, {3, 4, 5, 12, 15, 21}}

a(13)={117, True, {1, 2, 4, 6, 10}, {3, 5, 8, 9, 12, 15, 18, 24}}

a(14)={127, True, {1, 2, 4, 7, 10, 14}, {3, 5, 6, 9, 12, 15, 18, 21}}

a(15)={147, True, {1, 2, 6, 7, 8, 10, 14}, {3, 4, 5, 9, 15, 18, 21, 24}}

a(16)={159, True, {1, 2, 3, 7, 10, 14}, {4, 5, 6, 8, 9, 12, 15, 18, 21, 24}}

a(17)={179, True, {1, 2, 3, 7, 8, 14}, {4, 5, 6, 9, 10, 12, 15, 18, 20, 21, 24}}

a(18)={207, True, {1, 2, 3, 6, 7, 21}, {4, 5, 8, 9, 10, 12, 14, 15, 18, 20, 24, 28}}

a(19)={225, True, {1, 2, 4, 6, 7, 10, 14}, {3, 5, 8, 9, 11, 12, 15, 18, 21, 22, 24, 33}}

a(20)={245, True, {1, 2, 4, 6, 7, 8, 14}, {3, 5, 9, 10, 11, 12, 15, 18, 20, 21, 22, 24, 33}}

a(21)={273, True, {1, 2, 3, 4, 7, 21}, {5, 6, 8, 9, 10, 11, 12, 14, 15, 18, 20, 22, 24, 28, 33}}

a(22)={303, True, {1, 2, 3, 6, 7, 10, 21}, {4, 5, 8, 9, 11, 12, 14, 15, 18, 20, 22, 24, 28, 30, 33}}

a(23)={337, True, {1, 2, 3, 6, 7, 8, 21}, {4, 5, 9, 10, 11, 12, 14, 15, 16, 18, 20, 22, 24, 28, 33, 48}}

a(24)={367, True, {1, 2, 4, 6, 7, 8, 10, 21}, {3, 5, 9, 11, 12, 14, 15, 16, 18, 20, 22, 24, 28, 30, 33, 48}}

a(25)={402, True, {1, 2, 3, 4, 8, 14, 15}, {5, 6, 7, 9, 10, 11, 12, 16, 18, 20, 21, 22, 24, 28, 30, 33, 35, 48}}

a(26)={438, True, {1, 2, 3, 4, 12, 14, 15, 18}, {5, 6, 7, 8, 9, 10, 11, 16, 20, 21, 22, 24, 28, 30, 33, 35, 36, 48}}

a(27)={478, True, {1, 2, 3, 4, 10, 14, 16, 18}, {5, 6, 7, 8, 9, 11, 12, 15, 20, 21, 22, 24, 28, 30, 33, 35, 36, 40, 48}}

a(28)={519, True, {1, 2, 3, 4, 6, 14, 15}, {5, 7, 8, 9, 10, 11, 12, 16, 18, 20, 21, 22, 24, 27, 28, 30, 33, 35, 36, 48, 54}}

a(29)={532, True, {1, 2, 3, 4, 6, 14, 15, 26}, {5, 7, 8, 9, 10, 11, 12, 13, 16, 18, 20, 21, 22, 24, 28, 30, 33, 35, 39, 48, 52}}

a(30)={568, True, {1, 2, 3, 4, 8, 14, 15, 18, 26}, {5, 6, 7, 9, 10, 11, 12, 13, 16, 20, 21, 22, 24, 28, 30, 33, 35, 36, 39, 48, 52}}

a(31)={608, True, {1, 2, 3, 6, 8, 10, 14, 16, 18, 26}, {4, 5, 7, 9, 11, 12, 13, 15, 20, 21, 22, 24, 28, 30, 33, 35, 36, 39, 40, 48, 52}}

a(32)={649, True, {1, 2, 3, 4, 8, 12, 14, 15, 26}, {5, 6, 7, 9, 10, 11, 13, 16, 18, 20, 21, 22, 24, 27, 28, 30, 33, 35, 36, 39, 48, 52, 54}}

a(33)={689, True, {1, 2, 3, 4, 8, 10, 14, 16, 26}, {5, 6, 7, 9, 11, 12, 13, 15, 18, 20, 21, 22, 24, 27, 28, 30, 33, 35, 36, 39, 40, 48, 52, 54}}

a(34)={731, True, {1, 2, 3, 4, 8, 10, 12, 16, 26}, {5, 6, 7, 9, 11, 13, 14, 15, 18, 20, 21, 22, 24, 27, 28, 30, 33, 35, 36, 39, 40, 42, 48, 52, 54}}

a(35)={775, True, {1, 2, 3, 4, 10, 11, 12, 16, 22, 26}, {5, 6, 7, 8, 9, 13, 14, 15, 18, 20, 21, 24, 27, 28, 30, 33, 35, 36, 39, 40, 42, 44, 48, 52, 54}}

a(36)={820, True, {1, 2, 3, 4, 6, 10, 16, 18, 26, 51}, {5, 7, 8, 9, 11, 12, 13, 14, 15, 17, 20, 21, 22, 24, 28, 30, 33, 34, 35, 36, 39, 40, 42, 48, 52, 68}}
a(36)={863, True, {2, 3, 4, 6, 8, 9, 10, 11, 12, 15, 16, 18, 22, 26, 51}, {5, 7, 13, 14, 17, 20, 21, 24, 28, 30, 33, 34, 35, 36, 39, 40, 42, 44, 48, 52, 68}}
a(37)={864, True, {1, 2, 3, 6, 8, 10, 11, 16, 18, 22, 26, 51}, {4, 5, 7, 9, 12, 13, 14, 15, 17, 20, 21, 24, 28, 30, 33, 34, 35, 36, 39, 40, 42, 44, 48, 52, 68}}        
a(37)={908, True, {2, 3, 4, 6, 8, 9, 10, 11, 12, 15, 16, 18, 22, 26, 51}, {5, 7, 13, 14, 17, 20, 21, 24, 28, 30, 33, 34, 35, 36, 39, 40, 42, 44, 45, 48, 52, 68}}
a(38)={909, True, {1, 2, 3, 4, 8, 11, 12, 16, 22, 26, 51}, {5, 6, 7, 9, 10, 13, 14, 15, 17, 18, 20, 21, 24, 28, 30, 33, 34, 35, 36, 39, 40, 42, 44, 45, 48, 52, 68}}
a(38)={962, True, {2, 3, 4, 5, 6, 8, 9, 11, 12, 16, 20, 22, 26, 51}, {7, 10, 13, 14, 15, 17, 18, 21, 24, 28, 30, 33, 34, 35, 36, 39, 40, 42, 44, 45, 48, 52, 54, 68}}
a(39)=
a(39)={989, True, {2, 3, 4, 5, 6, 8, 9, 11, 12, 16, 20, 22, 26, 51}, {7, 10, 13, 14, 15, 17, 18, 21, 24, 27, 28, 30, 33, 34, 35, 36, 39, 40, 42, 44, 45, 48, 52, 54, 68}}
a(40)=
a(40)={1044, True, {2, 3, 4, 6, 7, 8, 9, 10, 12, 15, 16, 21, 22, 26, 51}, {5, 11, 13, 14, 17, 18, 20, 24, 27, 28, 30, 33, 34, 35, 36, 39, 40, 42, 44, 45, 48, 52, 54, 55, 68}}
a(41)=
a(41)={1114, True, {2, 3, 4, 6, 7, 8, 9, 10, 12, 15, 16, 21, 22, 26, 51}, {5, 11, 13, 14, 17, 18, 20, 24, 27, 28, 30, 33, 34, 35, 36, 39, 40, 42, 44, 45, 48, 52, 54, 55, 68, 70}}
a(42)=
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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王守恩
 楼主| 发表于 2026-2-12 17:40:09 | 显示全部楼层
找一个数字串(有无限项), 满足 n 项倒数和(允许 "+" 或 "-" ) = 1。a(n) =  n 项最小和。——OEIS还没有。

先把前面搞清楚——后面应该不会难。

a(03)=11, {2, 3, 6}, {}}

a(04)=12=11+1, {1, 2}, {3, 6}

a(05)=22=12-6+4+12, {1, 3, 4}, {2, 12}

a(06)=28=22+6, {1, 2, 6}, {3, 4, 12}

a(07)=41=28-12+5+20, {1, 2, 4}, {3, 5, 6, 20}

a(08)=51=41+10, {1, 2, 5, 10}, {3, 4, 6, 20}

a(09)=58=51-20+12+15, {1, 2, 4, 10}, {3, 5, 6, 12, 15}

a(10)=78=58-12+8+24, {1, 2, 6, 8, 10}, {3, 4, 5, 15, 24}

a(11)=85=78-8-24+9+12+18, {1, 2, 3, 10}, {4, 5, 6, 9, 12, 15, 18}

a(12)=100=85-9-18+7+14+21, {1, 2, 6, 7, 10, 14}, {3, 4, 5, 12, 15, 21}

a(13)=117=100-7-14-21+8+9+18+24, {1, 2, 4, 6, 10}, {3, 5, 8, 9, 12, 15, 18, 24}

a(14)=127=117-8-24+7+14+21, {1, 2, 4, 7, 10, 14}, {3, 5, 6, 9, 12, 15, 18, 21}

a(15)=147=127-12+8+24, {1, 2, 6, 7, 8, 10, 14}, {3, 4, 5, 9, 15, 18, 21, 24}

a(16)=159=147+12, {1, 2, 3, 7, 10, 14}, {4, 5, 6, 8, 9, 12, 15, 18, 21, 24}

a(17)=179=159+20, {1, 2, 3, 7, 8, 14}, {4, 5, 6, 9, 10, 12, 15, 18, 20, 21, 24}

a(18)=207=179+28, {1, 2, 3, 6, 7, 21}, {4, 5, 8, 9, 10, 12, 14, 15, 18, 20, 24, 28}

a(19)=225=207-20-28+11+22+33, {1, 2, 4, 6, 7, 10, 14}, {3, 5, 8, 9, 11, 12, 15, 18, 21, 22, 24, 33}

a(20)=245=225+20, {1, 2, 4, 6, 7, 8, 14}, {3, 5, 9, 10, 11, 12, 15, 18, 20, 21, 22, 24, 33}

a(21)=273=245+28, {1, 2, 3, 4, 7, 21}, {5, 6, 8, 9, 10, 11, 12, 14, 15, 18, 20, 22, 24, 28, 33}

a(22)=303=273+30, {1, 2, 3, 6, 7, 10, 21}, {4, 5, 8, 9, 11, 12, 14, 15, 18, 20, 22, 24, 28, 30, 33}

a(23)=337=303-30+16+48, {1, 2, 3, 6, 7, 8, 21}, {4, 5, 9, 10, 11, 12, 14, 15, 16, 18, 20, 22, 24, 28, 33, 48}

a(24)=367=337+30, {1, 2, 4, 6, 7, 8, 10, 21}, {3, 5, 9, 11, 12, 14, 15, 16, 18, 20, 22, 24, 28, 30, 33, 48}

a(25)=402=367+35, {1, 2, 3, 4, 8, 14, 15}, {5, 6, 7, 9, 10, 11, 12, 16, 18, 20, 21, 22, 24, 28, 30, 33, 35, 48}

a(26)=438=402+36, {1, 2, 3, 4, 12, 14, 15, 18}, {5, 6, 7, 8, 9, 10, 11, 16, 20, 21, 22, 24, 28, 30, 33, 35, 36, 48}

a(27)=471=438-35-36+13+39+52, {1, 2, 3, 6, 7, 10, 13, 21, 39}, {4, 5, 8, 9, 11, 12, 14, 15, 16, 18, 20, 22, 24, 28, 30, 33, 48, 52}

a(28)=497=471+26, {1, 2, 3, 4, 7, 10, 21, 26}, {5, 6, 8, 9, 11, 12, 13, 14, 15, 16, 18, 20, 22, 24, 28, 30, 33, 39, 48, 52}

a(29)=532=497+35, {1, 2, 3, 4, 6, 14, 15, 26}, {5, 7, 8, 9, 10, 11, 12, 13, 16, 18, 20, 21, 22, 24, 28, 30, 33, 35, 39, 48, 52}

a(30)=568=532+36, {1, 2, 3, 4, 8, 14, 15, 18, 26}, {5, 6, 7, 9, 10, 11, 12, 13, 16, 20, 21, 22, 24, 28, 30, 33, 35, 36, 39, 48, 52}

a(31)=608=568+40, {1, 2, 3, 6, 8, 10, 14, 16, 18, 26}, {4, 5, 7, 9, 11, 12, 13, 15, 20, 21, 22, 24, 28, 30, 33, 35, 36, 39, 40, 48, 52}

a(32)=649=608-40+27+54, {1, 2, 3, 4, 8, 12, 14, 15, 26}, {5, 6, 7, 9, 10, 11, 13, 16, 18, 20, 21, 22, 24, 27, 28, 30, 33, 35, 36, 39, 48, 52, 54}

a(33)=689=649+40, {1, 2, 3, 4, 8, 10, 14, 16, 26}, {5, 6, 7, 9, 11, 12, 13, 15, 18, 20, 21, 22, 24, 27, 28, 30, 33, 35, 36, 39, 40, 48, 52, 54}

a(34)=731=689+42, {1, 2, 3, 4, 8, 10, 12, 16, 26}, {5, 6, 7, 9, 11, 13, 14, 15, 18, 20, 21, 22, 24, 27, 28, 30, 33, 35, 36, 39, 40, 42, 48, 52, 54}

a(35)=775=731+44, {1, 2, 3, 4, 10, 11, 12, 16, 22, 26}, {5, 6, 7, 8, 9, 13, 14, 15, 18, 20, 21, 24, 27, 28, 30, 33, 35, 36, 39, 40, 42, 44, 48, 52, 54}

a(36)=820=775-27-44-54+17+34+51+68, {1, 2, 3, 4, 6, 10, 16, 18, 26, 51}, {5, 7, 8, 9, 11, 12, 13, 14, 15, 17, 20, 21, 22, 24, 28, 30, 33, 34, 35, 36, 39, 40, 42, 48, 52, 68}

a(37)=864=820+44, {1, 2, 3, 6, 8, 10, 11, 16, 18, 22, 26, 51}, {4, 5, 7, 9, 12, 13, 14, 15, 17, 20, 21, 24, 28, 30, 33, 34, 35, 36, 39, 40, 42, 44, 48, 52, 68}        

a(38)=909=864+45, {1, 2, 3, 4, 8, 11, 12, 16, 22, 26, 51}, {5, 6, 7, 9, 10, 13, 14, 15, 17, 18, 20, 21, 24, 28, 30, 33, 34, 35, 36, 39, 40, 42, 44, 45, 48, 52, 68}

a(39)=963=909+54, {1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 16, 20, 22, 26, 51}, {7, 10, 13, 14, 15, 17, 18, 21, 24, 28, 30, 33, 34, 35, 36, 39, 40, 42, 44, 45, 48, 52, 54, 68}

a(40)=990=963+27, {1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 16, 20, 22, 26, 51}, {7, 10, 13, 14, 15, 17, 18, 21, 24, 27, 28, 30, 33, 34, 35, 36, 39, 40, 42, 44, 45, 48, 52, 54, 68}

a(41)=1045=990+55, {1, 2, 3, 4, 8, 9, 10, 16, 22, 26, 51}, {5, 6, 7, 11, 12, 13, 14, 15, 17, 18, 20, 21, 24, 27, 28, 30, 33, 34, 35, 36, 39, 40, 42, 44, 45, 48, 52, 54, 55, 68}

a(42)=1115=1045+70, {1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 15, 16, 21, 22, 26, 51}, {5, 11, 13, 14, 17, 18, 20, 24, 27, 28, 30, 33, 34, 35, 36, 39, 40, 42, 44, 45, 48, 52, 54, 55, 68, 70}

a(43)=1187=1115+72, {1, 2, 3, 4, 6, 7, 18, 21, 22, 26, 51}, {5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 24, 27, 28, 30, 33, 34, 35, 36, 39, 40, 42, 44, 45, 48, 52, 54, 55, 68, 70, 72}
a(44)=
a(45)=
a(46)=
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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王守恩
 楼主| 发表于 2026-2-13 10:03:49 | 显示全部楼层
接楼上。——往前看:  每个素数都可以有解。

05-5+01=1,    05+5+01=11,
10-5+02=7,    10+5+02=17,——1/10=((10+5+2)/10)/17=1/17+1/34+1/85=1/10
15-5+03=13,  15+5+03=23,
20-5+04=19,  20+5+04=29,
25-5+05=25,  25+5+05=35,
30-5+06=31,  30+5+06=41,
35-5+07=37,  35+5+07=47,
40-5+08=43,  40+5+08=53,
45-5+09=49,  45+5+09=59,
50-5+10=55,  50+5+10=65,
55-5+11=61,  55+5+11=71,
60-5+12=67,  60+5+12=77,
65-5+13=73,  65+5+13=83,
70-5+14=79,  70+5+14=89,
75-5+15=85,  75+5+15=95,
80-5+16=91,  80+5+16=101,
85-5+17=97,  85+5+17=107,
90-5+18=103,90+5+18=113,
95-5+19=109,95+5+19=119,
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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