有这样一串数(OEIS找不到)

mathe · 发表于 2024-5-12 06:37:56

N=10
2075673600=1*2*3*7*15*16*18*20*22*26=4*5*6*8*9*10*11*12*13*14
N=11(没有验证最小)
58118860800=1*2*3*4*15*20*21*22*24*26*28=5*6*7*8*9*10*11*12*13*14*16
N=12(没有验证最小)
1270312243200=1*2*3*4*14*15*20*22*24*26*27*34=5*6*7*8*9*10*11*12*13*16*17*18
N=13(没有验证最小)
29640619008000=1*2*3*4*9*20*21*22*24*25*26*28*34=5*6*7*8*10*11*12*13*14*15*16*17*18
N=14(没有验证最小)
844757641728000=1*2*3*4*6*20*21*22*25*26*27*28*34*38=5*7*8*9*10*11*12*13*14*15*16*17*18*19

王守恩 · 发表于 2024-5-12 08:13:46

N=02, 02*03=06,
N=03, N(02)*(06.0)(3*2)=36,
N=04, N(03)*(06.7)(5*4/3)=240,
N=05, N(04)*(10.5)(7*3/2)=2520,
N=06, N(05)*(12.0)(4*3)=30240,
N=07, N(06)*(14.7)(11*4/3)=443520,
N=08, N(07)*(15.0)(5*3)=6652800,
N=09, N(08)*(20.0)(5*4)=133056000,
N=10, N(09)*(15.6)(13*3*2/5)=2075673600,
N=11, N(10)*(28.0)(7*4)=58118860800,
N=12, N(11)*(21.9)(17*9/7)=1270312243200,
N=13, N(12)*(23.3)(7*5*2/3)=29640619008000,
N=14, N(13)*(28.5)(19*3/2)=844757641728000,

王守恩 · 发表于 2024-5-12 13:00:40

譬如: N=11, N(10)*(28.0)(7*4)=58118860800,
Z[Sqrt[25!/(17*19*23)]]
Z[4790016000 Sqrt[91]]
Z[Sqrt[26!/(14*17*19*23)]]
Z[62270208000]
Z[Sqrt[27!/(17*18*19*21*23)]]
Z[62270208000]
Z[Sqrt[28!/(17*18*19*23*25*27)]]
Z[58118860800]
Z[Sqrt[29!/(14*17*19*23*27*28*29)]]
Z[62270208000]
Z[Sqrt[30!/(17*19*20*21*23*27*28*29)]]
Z[62270208000]
Z[Sqrt[31!/(17*19*20*21*23*27*28*29*31)]]
Z[62270208000]
Z[Sqrt[32!/(14*17*18*19*23*27*28*29*30*31)]]
Z[83026944000]
Z[Sqrt[33!/(14*17*18*19*23*27*28*29*30*31*33)]]
[83026944000]
Z[Sqrt[34!/(14*18*19*23*25*27*28*29*30*31*32*33)]]
Z[70572902400]
Z[Sqrt[35!/(14*18*19*23*25*27*28*29*30*31*32*33*35)]]
Z[70572902400]
Z[Sqrt[36!/(14*17*19*23*25*27*28*29*30*31*32*33*34*35)]]
Z[74724249600]
Z[Sqrt[37!/(14*17*19*23*25*27*28*29*30*31*32*33*34*35*37)]]
Z[74724249600]
Z[Sqrt[38!/(8*14*17*23*25*27*28*29*30*31*32*33*34*35*36*37)]]
Z[118313395200]

mathe · 发表于 2024-5-12 16:40:45

如果x可以写成两组互不相交的不同n个整数的乘积。那么这2n个不同整数的乘积为$x^2$.
所以我们可以先试着寻找m个不同整数乘积能够得出最小的完全平方数开根号后的取值，看看和本体之间有什么关联:
N=1:1
N=2:2
N=3:4
N=4:6
N=5:12
N=6:36
N=7:120
N=8:240
N=9:720
N=10:2520
N=11:10080
N=12:30240
N=13:110880
N=14:443520
N=15:1814400
N=16:6652800
N=17:26611200
N=18:133056000
N=19:518918400
N=20:2075673600
N=21:10378368000
N=22:58118860800
N=23:261534873600
N=24:1270312243200
N=25:5928123801600
N=26:29640619008000
N=27:177843714048000
N=28:965437304832000
N=29:5068545850368000
N=30:30411275102208000
N=31:202741834014720000
N=32:1216451004088320000
可以看出这个N=2n对应的结果应该和本题所求的结果是相同的
所以我们可以先试着优化这个问题的结果（相对容易很多），然后验证对应的值存在一种方案可以拆分成两组各自n个数，它们乘积相等

mathe · 发表于 2024-5-12 21:29:46

找到bug了，修改以后为:
N=1:1
N=2:2
N=3:4
N=4:6
N=5:12
N=6:36
N=7:120
N=8:240
N=9:720
N=10:2520
N=11:10080
N=12:30240
N=13:110880
N=14:443520
N=15:1814400
N=16:6652800
N=17:26611200
N=18:133056000
N=19:518918400
N=20:2075673600
N=21:10378368000
N=22:58118860800
N=23:261534873600
N=24:1270312243200
N=25:5928123801600
N=26:29640619008000
N=27:168951528345600
N=28:844757641728000
N=29:4505374089216000
N=30:25342729251840000
N=31:152056375511040000
N=32:1216451004088320000

northwolves · 发表于 2024-5-12 22:37:33

N=15,稍小一点的解：25342729251840000={1,2,3,4,5,20,21,22,24,26,27,30,34,35,38} {6,7,8,9,10,11,12,13,14,15,16,17,18,19,25}

northwolves · 发表于 2024-5-12 22:45:35

N=16,稍小一点的解：810967336058880000={1, 2, 3, 4, 5, 20, 21, 22, 24, 26, 27, 28, 30, 34, 38, 40} {6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 25, 32}

northwolves · 发表于 2024-5-12 22:53:35

N=17 27978373094031360000={1,2,3,4,5,21,22,23,24,25,26,27,28,32,34,38,45} {6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,30,46}

northwolves · 发表于 2024-5-12 23:03:33

N=18 1077167364120207360000={1,2,3,4,5,6,24,25,26,27,28,33,34,35,38,42,44,46} {7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,30}

northwolves · 发表于 2024-5-12 23:14:24

N=19 43086694564808294400000={1,2,3,4,5,6,21,26,27,28,30,32,33,34,35,38,44,46,50} {7,8,9,10,11,12,13,14,15,16,17,18,19,20,22,23,24,25,42}

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[求助] 有这样一串数(OEIS找不到)

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