连分数的难题

markfang2050 · 发表于 2019-9-19 21:22:40

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如图，不限制自然数范围，求出所有解（集合，不排序）的个数。

.·.·. · 发表于 2019-9-20 12:52:08

如果是6个不同的，没记错第一个一定是1/2
然后剩下的搜就是了
坛子里有搜的方法与理论

如果约定前面的分母比后面的小，那么，当前面k个分母给定之后，后面的分数之和的上界也就给定了
我们可以借助这个上界划定搜索范围

然后剩下的就是搜了

zeroieme · 发表于 2019-9-20 13:08:07

不是连分数，这个叫埃及分数。

mathe · 发表于 2019-9-20 13:30:18

https://bbs.emath.ac.cn/thread-223-2-1.html

mathe · 发表于 2019-9-20 15:28:12

计算结果好像2320组解
比如有
1/2 +1/3 +1/7 +1/43 +1/1807 +1/3263442
1/2 +1/3 +1/7 +1/43 +1/1808 +1/1632624
1/2 +1/3 +1/7 +1/43 +1/1809 +1/1089018
1/2 +1/3 +1/7 +1/43 +1/1810 +1/817215
1/2 +1/3 +1/7 +1/43 +1/1812 +1/545412
1/2 +1/3 +1/7 +1/43 +1/1813 +1/467754
1/2 +1/3 +1/7 +1/43 +1/1815 +1/364210
1/2 +1/3 +1/7 +1/43 +1/1818 +1/273609
1/2 +1/3 +1/7 +1/43 +1/1820 +1/234780
1/2 +1/3 +1/7 +1/43 +1/1824 +1/183008
1/2 +1/3 +1/7 +1/43 +1/1827 +1/157122
1/2 +1/3 +1/7 +1/43 +1/1834 +1/118293
1/2 +1/3 +1/7 +1/43 +1/1842 +1/92407
...
1/3 +1/4 +1/5 +1/9 +1/18 +1/20
1/3 +1/4 +1/5 +1/10 +1/12 +1/30
1/3 +1/4 +1/5 +1/10 +1/15 +1/20
1/3 +1/4 +1/6 +1/7 +1/10 +1/140
1/3 +1/4 +1/6 +1/7 +1/12 +1/42
1/3 +1/4 +1/6 +1/7 +1/14 +1/28
1/3 +1/4 +1/6 +1/8 +1/9 +1/72
1/3 +1/4 +1/6 +1/8 +1/10 +1/40
1/3 +1/4 +1/6 +1/8 +1/12 +1/24
1/3 +1/4 +1/6 +1/9 +1/12 +1/18
1/3 +1/4 +1/6 +1/10 +1/12 +1/15

markfang2050 · 发表于 2019-9-20 16:01:27

mathe 发表于 2019-9-20 15:28
计算结果好像2320组解
比如有
1/2 +1/3 +1/7 +1/43 +1/1807 +1/3263442

2320是对的。MMA验证过。你的程序能否发下看看？

markfang2050 · 发表于 2019-9-20 19:56:14

{{2, 3, 7, 43, 1807, 3263442}, {2, 3, 7, 43, 1808, 1632624}, {2, 3, 7,
43, 1809, 1089018}, {2, 3, 7, 43, 1810, 817215}, {2, 3, 7, 43,
1812, 545412}, {2, 3, 7, 43, 1813, 467754}, {2, 3, 7, 43, 1815,
364210}, {2, 3, 7, 43, 1818, 273609}, {2, 3, 7, 43, 1820,
234780}, {2, 3, 7, 43, 1824, 183008}, {2, 3, 7, 43, 1827,
157122}, {2, 3, 7, 43, 1834, 118293}, {2, 3, 7, 43, 1842,
92407}, {2, 3, 7, 43, 1848, 79464}, {2, 3, 7, 43, 1849, 77658}, {2,
3, 7, 43, 1855, 68370}, {2, 3, 7, 43, 1869, 53578}, {2, 3, 7, 43,
1890, 40635}, {2, 3, 7, 43, 1892, 39732}, {2, 3, 7, 43, 1904,
35088}, {2, 3, 7, 43, 1932, 27692}, {2, 3, 7, 43, 1935, 27090}, {2,
3, 7, 43, 1953, 23994}, {2, 3, 7, 43, 1978, 20769}, {2, 3, 7, 43,
2002, 18447}, {2, 3, 7, 43, 2058, 14749}, {2, 3, 7, 43, 2064,
14448}, {2, 3, 7, 43, 2100, 12900}, {2, 3, 7, 43, 2107, 12642}, {2,
3, 7, 43, 2193, 10234}, {2, 3, 7, 43, 2247, 9202}, {2, 3, 7, 43,
2322, 8127}, {2, 3, 7, 43, 2394, 7353}, {2, 3, 7, 43, 2408,
7224}, {2, 3, 7, 43, 2580, 6020}, {2, 3, 7, 43, 2688, 5504}, {2, 3,
7, 43, 2709, 5418}, {2, 3, 7, 43, 3010, 4515}, {2, 3, 7, 43, 3354,
3913}, {2, 3, 7, 43, 3570, 3655}, {2, 3, 7, 44, 925, 854700}, {2,
3, 7, 44, 926, 427812}, {2, 3, 7, 44, 927, 285516}, {2, 3, 7, 44,
928, 214368}, {2, 3, 7, 44, 930, 143220}, {2, 3, 7, 44, 931,
122892}, {2, 3, 7, 44, 932, 107646}, {2, 3, 7, 44, 933, 95788}, {2,
3, 7, 44, 935, 78540}, {2, 3, 7, 44, 936, 72072}, {2, 3, 7, 44,
938, 61908}, {2, 3, 7, 44, 940, 54285}, {2, 3, 7, 44, 942,
48356}, {2, 3, 7, 44, 945, 41580}, {2, 3, 7, 44, 946, 39732}, {2,
3, 7, 44, 948, 36498}, {2, 3, 7, 44, 952, 31416}, {2, 3, 7, 44,
957, 26796}, {2, 3, 7, 44, 960, 24640}, {2, 3, 7, 44, 966,
21252}, {2, 3, 7, 44, 968, 20328}, {2, 3, 7, 44, 972, 18711}, {2,
3, 7, 44, 973, 18348}, {2, 3, 7, 44, 980, 16170}, {2, 3, 7, 44,
987, 14476}, {2, 3, 7, 44, 990, 13860}, {2, 3, 7, 44, 996,
12782}, {2, 3, 7, 44, 1001, 12012}, {2, 3, 7, 44, 1008, 11088}, {2,
3, 7, 44, 1012, 10626}, {2, 3, 7, 44, 1022, 9636}, {2, 3, 7, 44,
1023, 9548}, {2, 3, 7, 44, 1036, 8547}, {2, 3, 7, 44, 1045,
7980}, {2, 3, 7, 44, 1050, 7700}, {2, 3, 7, 44, 1056, 7392}, {2, 3,
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672, 10080}, {2, 3, 7, 45, 675, 9450}, {2, 3, 7, 45, 679,
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6300}, {2, 3, 7, 45, 705, 5922}, {2, 3, 7, 45, 711, 5530}, {2, 3,
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4680}, {2, 3, 7, 45, 730, 4599}, {2, 3, 7, 45, 735, 4410}, {2, 3,
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2898}, {2, 3, 7, 45, 810, 2835}, {2, 3, 7, 45, 819, 2730}, {2, 3,
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2394}, {2, 3, 7, 45, 875, 2250}, {2, 3, 7, 45, 882, 2205}, {2, 3,
7, 45, 900, 2100}, {2, 3, 7, 45, 924, 1980}, {2, 3, 7, 45, 930,
1953}, {2, 3, 7, 45, 945, 1890}, {2, 3, 7, 45, 954, 1855}, {2, 3,
7, 45, 980, 1764}, {2, 3, 7, 45, 1008, 1680}, {2, 3, 7, 45, 1035,
1610}, {2, 3, 7, 45, 1050, 1575}, {2, 3, 7, 45, 1071, 1530}, {2, 3,
7, 45, 1080, 1512}, {2, 3, 7, 45, 1120, 1440}, {2, 3, 7, 45, 1155,
1386}, {2, 3, 7, 45, 1170, 1365}, {2, 3, 7, 45, 1197, 1330}, {2,
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486, 78246}, {2, 3, 7, 46, 490, 33810}, {2, 3, 7, 46, 492,
26404}, {2, 3, 7, 46, 504, 11592}, {2, 3, 7, 46, 506, 10626}, {2,
3, 7, 46, 532, 5244}, {2, 3, 7, 46, 546, 4186}, {2, 3, 7, 46, 552,
3864}, {2, 3, 7, 46, 630, 2070}, {2, 3, 7, 46, 644, 1932}, {2, 3,
7, 46, 690, 1610}, {2, 3, 7, 46, 924, 1012}, {2, 3, 7, 47, 395,
779730}, {2, 3, 7, 47, 396, 130284}, {2, 3, 7, 47, 399, 37506}, {2,
3, 7, 47, 402, 22043}, {2, 3, 7, 47, 420, 6580}, {2, 3, 7, 47,
423, 5922}, {2, 3, 7, 47, 434, 4371}, {2, 3, 7, 47, 483, 2162}, {2,
3, 7, 47, 564, 1316}, {2, 3, 7, 47, 658, 987}, {2, 3, 7, 48, 337,
113232}, {2, 3, 7, 48, 338, 56784}, {2, 3, 7, 48, 339, 37968}, {2,
3, 7, 48, 340, 28560}, {2, 3, 7, 48, 342, 19152}, {2, 3, 7, 48,
343, 16464}, {2, 3, 7, 48, 344, 14448}, {2, 3, 7, 48, 345,
12880}, {2, 3, 7, 48, 348, 9744}, {2, 3, 7, 48, 350, 8400}, {2, 3,
7, 48, 352, 7392}, {2, 3, 7, 48, 354, 6608}, {2, 3, 7, 48, 357,
5712}, {2, 3, 7, 48, 360, 5040}, {2, 3, 7, 48, 364, 4368}, {2, 3,
7, 48, 368, 3864}, {2, 3, 7, 48, 372, 3472}, {2, 3, 7, 48, 378,
3024}, {2, 3, 7, 48, 384, 2688}, {2, 3, 7, 48, 385, 2640}, {2, 3,
7, 48, 392, 2352}, {2, 3, 7, 48, 399, 2128}, {2, 3, 7, 48, 400,
2100}, {2, 3, 7, 48, 408, 1904}, {2, 3, 7, 48, 420, 1680}, {2, 3,
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7, 50, 315, 1575}, {2, 3, 7, 50, 325, 1365}, {2, 3, 7, 50, 336,
1200}, {2, 3, 7, 50, 350, 1050}, {2, 3, 7, 50, 375, 875}, {2, 3, 7,
50, 385, 825}, {2, 3, 7, 50, 420, 700}, {2, 3, 7, 50, 450,
630}, {2, 3, 7, 50, 483, 575}, {2, 3, 7, 51, 239, 56882}, {2, 3, 7,
51, 240, 28560}, {2, 3, 7, 51, 242, 14399}, {2, 3, 7, 51, 245,
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51, 357, 714}, {2, 3, 7, 51, 434, 527}, {2, 3, 7, 52, 219,
79716}, {2, 3, 7, 52, 220, 30030}, {2, 3, 7, 52, 221, 18564}, {2,
3, 7, 52, 222, 13468}, {2, 3, 7, 52, 224, 8736}, {2, 3, 7, 52, 228,
5187}, {2, 3, 7, 52, 231, 4004}, {2, 3, 7, 52, 234, 3276}, {2, 3,
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1365}, {2, 3, 7, 52, 273, 1092}, {2, 3, 7, 52, 286, 924}, {2, 3, 7,
52, 312, 728}, {2, 3, 7, 52, 336, 624}, {2, 3, 7, 52, 364,
546}, {2, 3, 7, 52, 420, 455}, {2, 3, 7, 53, 203, 64554}, {2, 3, 7,
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24, 78, 936}, {2, 3, 9, 24, 80, 720}, {2, 3, 9, 24, 81, 648}, {2,
3, 9, 24, 84, 504}, {2, 3, 9, 24, 88, 396}, {2, 3, 9, 24, 90,
360}, {2, 3, 9, 24, 96, 288}, {2, 3, 9, 24, 99, 264}, {2, 3, 9, 24,
104, 234}, {2, 3, 9, 24, 108, 216}, {2, 3, 9, 24, 120, 180}, {2,
3, 9, 24, 126, 168}, {2, 3, 9, 24, 136, 153}, {2, 3, 9, 25, 65,
5850}, {2, 3, 9, 25, 66, 2475}, {2, 3, 9, 25, 72, 600}, {2, 3, 9,
25, 75, 450}, {2, 3, 9, 25, 90, 225}, {2, 3, 9, 25, 100, 180}, {2,
3, 9, 26, 59, 6903}, {2, 3, 9, 26, 60, 2340}, {2, 3, 9, 26, 63,
819}, {2, 3, 9, 26, 65, 585}, {2, 3, 9, 26, 72, 312}, {2, 3, 9, 26,
78, 234}, {2, 3, 9, 26, 99, 143}, {2, 3, 9, 27, 55, 2970}, {2, 3,
9, 27, 56, 1512}, {2, 3, 9, 27, 57, 1026}, {2, 3, 9, 27, 58,
783}, {2, 3, 9, 27, 60, 540}, {2, 3, 9, 27, 63, 378}, {2, 3, 9, 27,
66, 297}, {2, 3, 9, 27, 72, 216}, {2, 3, 9, 27, 81, 162}, {2, 3,
9, 27, 90, 135}, {2, 3, 9, 28, 51, 4284}, {2, 3, 9, 28, 52,
1638}, {2, 3, 9, 28, 54, 756}, {2, 3, 9, 28, 56, 504}, {2, 3, 9,
28, 60, 315}, {2, 3, 9, 28, 63, 252}, {2, 3, 9, 28, 70, 180}, {2,
3, 9, 28, 72, 168}, {2, 3, 9, 28, 84, 126}, {2, 3, 9, 29, 48,
4176}, {2, 3, 9, 29, 58, 261}, {2, 3, 9, 30, 46, 2070}, {2, 3, 9,
30, 48, 720}, {2, 3, 9, 30, 50, 450}, {2, 3, 9, 30, 54, 270}, {2,
3, 9, 30, 60, 180}, {2, 3, 9, 30, 70, 126}, {2, 3, 9, 30, 72,
120}, {2, 3, 9, 31, 43, 23994}, {2, 3, 9, 31, 45, 930}, {2, 3, 9,
32, 42, 2016}, {2, 3, 9, 32, 45, 480}, {2, 3, 9, 32, 48, 288}, {2,
3, 9, 32, 72, 96}, {2, 3, 9, 33, 40, 3960}, {2, 3, 9, 33, 42,
693}, {2, 3, 9, 33, 44, 396}, {2, 3, 9, 33, 45, 330}, {2, 3, 9, 33,
66, 99}, {2, 3, 9, 33, 72, 88}, {2, 3, 9, 34, 39, 1989}, {2, 3, 9,
34, 45, 255}, {2, 3, 9, 34, 51, 153}, {2, 3, 9, 35, 40, 504}, {2,
3, 9, 35, 42, 315}, {2, 3, 9, 35, 45, 210}, {2, 3, 9, 35, 63,
90}, {2, 3, 9, 36, 37, 1332}, {2, 3, 9, 36, 38, 684}, {2, 3, 9, 36,
39, 468}, {2, 3, 9, 36, 40, 360}, {2, 3, 9, 36, 42, 252}, {2, 3,
9, 36, 44, 198}, {2, 3, 9, 36, 45, 180}, {2, 3, 9, 36, 48,
144}, {2, 3, 9, 36, 52, 117}, {2, 3, 9, 36, 54, 108}, {2, 3, 9, 36,
60, 90}, {2, 3, 9, 36, 63, 84}, {2, 3, 9, 39, 45, 130}, {2, 3, 9,
40, 45, 120}, {2, 3, 9, 40, 60, 72}, {2, 3, 9, 42, 45, 105}, {2, 3,
9, 42, 56, 72}, {2, 3, 9, 45, 48, 80}, {2, 3, 9, 45, 50, 75}, {2,
3, 9, 45, 55, 66}, {2, 3, 10, 16, 241, 57840}, {2, 3, 10, 16, 242,
29040}, {2, 3, 10, 16, 243, 19440}, {2, 3, 10, 16, 244, 14640}, {2,
3, 10, 16, 245, 11760}, {2, 3, 10, 16, 246, 9840}, {2, 3, 10, 16,
248, 7440}, {2, 3, 10, 16, 249, 6640}, {2, 3, 10, 16, 250,
6000}, {2, 3, 10, 16, 252, 5040}, {2, 3, 10, 16, 255, 4080}, {2, 3,
10, 16, 256, 3840}, {2, 3, 10, 16, 258, 3440}, {2, 3, 10, 16, 260,
3120}, {2, 3, 10, 16, 264, 2640}, {2, 3, 10, 16, 265, 2544}, {2,
3, 10, 16, 270, 2160}, {2, 3, 10, 16, 272, 2040}, {2, 3, 10, 16,
276, 1840}, {2, 3, 10, 16, 280, 1680}, {2, 3, 10, 16, 285,
1520}, {2, 3, 10, 16, 288, 1440}, {2, 3, 10, 16, 290, 1392}, {2, 3,
10, 16, 300, 1200}, {2, 3, 10, 16, 304, 1140}, {2, 3, 10, 16, 312,
1040}, {2, 3, 10, 16, 315, 1008}, {2, 3, 10, 16, 320, 960}, {2, 3,
10, 16, 330, 880}, {2, 3, 10, 16, 336, 840}, {2, 3, 10, 16, 340,
816}, {2, 3, 10, 16, 360, 720}, {2, 3, 10, 16, 368, 690}, {2, 3,
10, 16, 384, 640}, {2, 3, 10, 16, 390, 624}, {2, 3, 10, 16, 400,
600}, {2, 3, 10, 16, 420, 560}, {2, 3, 10, 16, 432, 540}, {2, 3,
10, 16, 440, 528}, {2, 3, 10, 16, 465, 496}, {2, 3, 10, 17, 128,
32640}, {2, 3, 10, 17, 129, 10965}, {2, 3, 10, 17, 130, 6630}, {2,
3, 10, 17, 132, 3740}, {2, 3, 10, 17, 135, 2295}, {2, 3, 10, 17,
136, 2040}, {2, 3, 10, 17, 140, 1428}, {2, 3, 10, 17, 150,
850}, {2, 3, 10, 17, 153, 765}, {2, 3, 10, 17, 165, 561}, {2, 3,
10, 17, 170, 510}, {2, 3, 10, 17, 204, 340}, {2, 3, 10, 17, 240,
272}, {2, 3, 10, 18, 91, 8190}, {2, 3, 10, 18, 92, 4140}, {2, 3,
10, 18, 93, 2790}, {2, 3, 10, 18, 94, 2115}, {2, 3, 10, 18, 95,
1710}, {2, 3, 10, 18, 96, 1440}, {2, 3, 10, 18, 99, 990}, {2, 3,
10, 18, 100, 900}, {2, 3, 10, 18, 102, 765}, {2, 3, 10, 18, 105,
630}, {2, 3, 10, 18, 108, 540}, {2, 3, 10, 18, 110, 495}, {2, 3,
10, 18, 115, 414}, {2, 3, 10, 18, 117, 390}, {2, 3, 10, 18, 120,
360}, {2, 3, 10, 18, 126, 315}, {2, 3, 10, 18, 135, 270}, {2, 3,
10, 18, 140, 252}, {2, 3, 10, 18, 144, 240}, {2, 3, 10, 18, 150,
225}, {2, 3, 10, 18, 165, 198}, {2, 3, 10, 18, 171, 190}, {2, 3,
10, 19, 72, 6840}, {2, 3, 10, 19, 75, 1425}, {2, 3, 10, 19, 76,
1140}, {2, 3, 10, 19, 90, 342}, {2, 3, 10, 19, 95, 285}, {2, 3, 10,
19, 114, 190}, {2, 3, 10, 20, 61, 3660}, {2, 3, 10, 20, 62,
1860}, {2, 3, 10, 20, 63, 1260}, {2, 3, 10, 20, 64, 960}, {2, 3,
10, 20, 65, 780}, {2, 3, 10, 20, 66, 660}, {2, 3, 10, 20, 68,
510}, {2, 3, 10, 20, 69, 460}, {2, 3, 10, 20, 70, 420}, {2, 3, 10,
20, 72, 360}, {2, 3, 10, 20, 75, 300}, {2, 3, 10, 20, 76, 285}, {2,
3, 10, 20, 78, 260}, {2, 3, 10, 20, 80, 240}, {2, 3, 10, 20, 84,
210}, {2, 3, 10, 20, 85, 204}, {2, 3, 10, 20, 90, 180}, {2, 3, 10,
20, 96, 160}, {2, 3, 10, 20, 100, 150}, {2, 3, 10, 20, 105,
140}, {2, 3, 10, 20, 108, 135}, {2, 3, 10, 20, 110, 132}, {2, 3,
10, 21, 53, 5565}, {2, 3, 10, 21, 54, 1890}, {2, 3, 10, 21, 55,
1155}, {2, 3, 10, 21, 56, 840}, {2, 3, 10, 21, 57, 665}, {2, 3, 10,
21, 60, 420}, {2, 3, 10, 21, 63, 315}, {2, 3, 10, 21, 65,
273}, {2, 3, 10, 21, 70, 210}, {2, 3, 10, 21, 75, 175}, {2, 3, 10,
21, 77, 165}, {2, 3, 10, 21, 84, 140}, {2, 3, 10, 21, 90, 126}, {2,
3, 10, 22, 48, 2640}, {2, 3, 10, 22, 50, 825}, {2, 3, 10, 22, 55,
330}, {2, 3, 10, 22, 60, 220}, {2, 3, 10, 22, 66, 165}, {2, 3, 10,
22, 90, 99}, {2, 3, 10, 23, 45, 1035}, {2, 3, 10, 23, 46, 690}, {2,
3, 10, 23, 69, 115}, {2, 3, 10, 24, 41, 1640}, {2, 3, 10, 24, 42,
840}, {2, 3, 10, 24, 44, 440}, {2, 3, 10, 24, 45, 360}, {2, 3, 10,
24, 48, 240}, {2, 3, 10, 24, 50, 200}, {2, 3, 10, 24, 56, 140}, {2,
3, 10, 24, 60, 120}, {2, 3, 10, 24, 65, 104}, {2, 3, 10, 24, 72,
90}, {2, 3, 10, 25, 38, 2850}, {2, 3, 10, 25, 39, 975}, {2, 3, 10,
25, 40, 600}, {2, 3, 10, 25, 42, 350}, {2, 3, 10, 25, 45, 225}, {2,
3, 10, 25, 50, 150}, {2, 3, 10, 25, 60, 100}, {2, 3, 10, 26, 36,
2340}, {2, 3, 10, 26, 39, 390}, {2, 3, 10, 26, 40, 312}, {2, 3, 10,
26, 65, 78}, {2, 3, 10, 27, 34, 4590}, {2, 3, 10, 27, 35,
945}, {2, 3, 10, 27, 36, 540}, {2, 3, 10, 27, 40, 216}, {2, 3, 10,
27, 45, 135}, {2, 3, 10, 27, 54, 90}, {2, 3, 10, 28, 33, 1540}, {2,
3, 10, 28, 35, 420}, {2, 3, 10, 28, 36, 315}, {2, 3, 10, 28, 40,
168}, {2, 3, 10, 28, 42, 140}, {2, 3, 10, 28, 60, 70}, {2, 3, 10,
30, 31, 930}, {2, 3, 10, 30, 32, 480}, {2, 3, 10, 30, 33, 330}, {2,
3, 10, 30, 34, 255}, {2, 3, 10, 30, 35, 210}, {2, 3, 10, 30, 36,
180}, {2, 3, 10, 30, 39, 130}, {2, 3, 10, 30, 40, 120}, {2, 3, 10,
30, 42, 105}, {2, 3, 10, 30, 45, 90}, {2, 3, 10, 30, 48, 80}, {2,
3, 10, 30, 50, 75}, {2, 3, 10, 30, 55, 66}, {2, 3, 10, 32, 40,
96}, {2, 3, 10, 33, 40, 88}, {2, 3, 10, 35, 42, 70}, {2, 3, 10, 35,
45, 63}, {2, 3, 10, 36, 40, 72}, {2, 3, 10, 36, 45, 60}, {2, 3,
10, 40, 42, 56}, {2, 3, 11, 14, 232, 53592}, {2, 3, 11, 14, 234,
18018}, {2, 3, 11, 14, 238, 7854}, {2, 3, 11, 14, 240, 6160}, {2,
3, 11, 14, 242, 5082}, {2, 3, 11, 14, 252, 2772}, {2, 3, 11, 14,
264, 1848}, {2, 3, 11, 14, 280, 1320}, {2, 3, 11, 14, 294,
1078}, {2, 3, 11, 14, 308, 924}, {2, 3, 11, 14, 330, 770}, {2, 3,
11, 14, 352, 672}, {2, 3, 11, 14, 378, 594}, {2, 3, 11, 15, 111,
12210}, {2, 3, 11, 15, 112, 6160}, {2, 3, 11, 15, 114, 3135}, {2,
3, 11, 15, 115, 2530}, {2, 3, 11, 15, 120, 1320}, {2, 3, 11, 15,
121, 1210}, {2, 3, 11, 15, 130, 715}, {2, 3, 11, 15, 132, 660}, {2,
3, 11, 15, 135, 594}, {2, 3, 11, 15, 154, 385}, {2, 3, 11, 15,
160, 352}, {2, 3, 11, 15, 165, 330}, {2, 3, 11, 15, 210, 231}, {2,
3, 11, 16, 76, 10032}, {2, 3, 11, 16, 77, 3696}, {2, 3, 11, 16, 78,
2288}, {2, 3, 11, 16, 80, 1320}, {2, 3, 11, 16, 88, 528}, {2, 3,
11, 16, 96, 352}, {2, 3, 11, 16, 110, 240}, {2, 3, 11, 16, 112,
231}, {2, 3, 11, 16, 132, 176}, {2, 3, 11, 17, 60, 3740}, {2, 3,
11, 17, 66, 561}, {2, 3, 11, 18, 50, 4950}, {2, 3, 11, 18, 51,
1683}, {2, 3, 11, 18, 54, 594}, {2, 3, 11, 18, 55, 495}, {2, 3, 11,
18, 63, 231}, {2, 3, 11, 18, 66, 198}, {2, 3, 11, 18, 90,
110}, {2, 3, 11, 19, 44, 2508}, {2, 3, 11, 20, 39, 8580}, {2, 3,
11, 20, 40, 1320}, {2, 3, 11, 20, 44, 330}, {2, 3, 11, 20, 55,
132}, {2, 3, 11, 20, 60, 110}, {2, 3, 11, 21, 36, 2772}, {2, 3, 11,
21, 42, 231}, {2, 3, 11, 21, 66, 77}, {2, 3, 11, 22, 34,
1122}, {2, 3, 11, 22, 36, 396}, {2, 3, 11, 22, 42, 154}, {2, 3, 11,
22, 44, 132}, {2, 3, 11, 23, 31, 47058}, {2, 3, 11, 23, 33,
506}, {2, 3, 11, 24, 30, 1320}, {2, 3, 11, 24, 32, 352}, {2, 3, 11,
24, 33, 264}, {2, 3, 11, 24, 40, 110}, {2, 3, 11, 24, 44, 88}, {2,
3, 11, 25, 28, 23100}, {2, 3, 11, 26, 27, 3861}, {2, 3, 11, 26,
33, 143}, {2, 3, 12, 13, 157, 24492}, {2, 3, 12, 13, 158,
12324}, {2, 3, 12, 13, 159, 8268}, {2, 3, 12, 13, 160, 6240}, {2,
3, 12, 13, 162, 4212}, {2, 3, 12, 13, 164, 3198}, {2, 3, 12, 13,
165, 2860}, {2, 3, 12, 13, 168, 2184}, {2, 3, 12, 13, 169,
2028}, {2, 3, 12, 13, 172, 1677}, {2, 3, 12, 13, 174, 1508}, {2, 3,
12, 13, 180, 1170}, {2, 3, 12, 13, 182, 1092}, {2, 3, 12, 13, 192,
832}, {2, 3, 12, 13, 195, 780}, {2, 3, 12, 13, 204, 663}, {2, 3,
12, 13, 208, 624}, {2, 3, 12, 13, 228, 494}, {2, 3, 12, 13, 234,
468}, {2, 3, 12, 13, 260, 390}, {2, 3, 12, 13, 273, 364}, {2, 3,
12, 13, 300, 325}, {2, 3, 12, 14, 85, 7140}, {2, 3, 12, 14, 86,
3612}, {2, 3, 12, 14, 87, 2436}, {2, 3, 12, 14, 88, 1848}, {2, 3,
12, 14, 90, 1260}, {2, 3, 12, 14, 91, 1092}, {2, 3, 12, 14, 92,
966}, {2, 3, 12, 14, 93, 868}, {2, 3, 12, 14, 96, 672}, {2, 3, 12,
14, 98, 588}, {2, 3, 12, 14, 100, 525}, {2, 3, 12, 14, 102,
476}, {2, 3, 12, 14, 105, 420}, {2, 3, 12, 14, 108, 378}, {2, 3,
12, 14, 112, 336}, {2, 3, 12, 14, 120, 280}, {2, 3, 12, 14, 126,
252}, {2, 3, 12, 14, 132, 231}, {2, 3, 12, 14, 133, 228}, {2, 3,
12, 14, 140, 210}, {2, 3, 12, 14, 147, 196}, {2, 3, 12, 14, 156,
182}, {2, 3, 12, 15, 61, 3660}, {2, 3, 12, 15, 62, 1860}, {2, 3,
12, 15, 63, 1260}, {2, 3, 12, 15, 64, 960}, {2, 3, 12, 15, 65,
780}, {2, 3, 12, 15, 66, 660}, {2, 3, 12, 15, 68, 510}, {2, 3, 12,
15, 69, 460}, {2, 3, 12, 15, 70, 420}, {2, 3, 12, 15, 72, 360}, {2,
3, 12, 15, 75, 300}, {2, 3, 12, 15, 76, 285}, {2, 3, 12, 15, 78,
260}, {2, 3, 12, 15, 80, 240}, {2, 3, 12, 15, 84, 210}, {2, 3, 12,
15, 85, 204}, {2, 3, 12, 15, 90, 180}, {2, 3, 12, 15, 96, 160}, {2,
3, 12, 15, 100, 150}, {2, 3, 12, 15, 105, 140}, {2, 3, 12, 15,
108, 135}, {2, 3, 12, 15, 110, 132}, {2, 3, 12, 16, 49, 2352}, {2,
3, 12, 16, 50, 1200}, {2, 3, 12, 16, 51, 816}, {2, 3, 12, 16, 52,
624}, {2, 3, 12, 16, 54, 432}, {2, 3, 12, 16, 56, 336}, {2, 3, 12,
16, 57, 304}, {2, 3, 12, 16, 60, 240}, {2, 3, 12, 16, 64, 192}, {2,
3, 12, 16, 66, 176}, {2, 3, 12, 16, 72, 144}, {2, 3, 12, 16, 80,
120}, {2, 3, 12, 16, 84, 112}, {2, 3, 12, 17, 41, 8364}, {2, 3, 12,
17, 42, 1428}, {2, 3, 12, 17, 44, 561}, {2, 3, 12, 17, 48,
272}, {2, 3, 12, 17, 51, 204}, {2, 3, 12, 17, 68, 102}, {2, 3, 12,
18, 37, 1332}, {2, 3, 12, 18, 38, 684}, {2, 3, 12, 18, 39,
468}, {2, 3, 12, 18, 40, 360}, {2, 3, 12, 18, 42, 252}, {2, 3, 12,
18, 44, 198}, {2, 3, 12, 18, 45, 180}, {2, 3, 12, 18, 48, 144}, {2,
3, 12, 18, 52, 117}, {2, 3, 12, 18, 54, 108}, {2, 3, 12, 18, 60,
90}, {2, 3, 12, 18, 63, 84}, {2, 3, 12, 19, 33, 2508}, {2, 3, 12,
19, 36, 342}, {2, 3, 12, 19, 38, 228}, {2, 3, 12, 19, 57, 76}, {2,
3, 12, 20, 31, 930}, {2, 3, 12, 20, 32, 480}, {2, 3, 12, 20, 33,
330}, {2, 3, 12, 20, 34, 255}, {2, 3, 12, 20, 35, 210}, {2, 3, 12,
20, 36, 180}, {2, 3, 12, 20, 39, 130}, {2, 3, 12, 20, 40, 120}, {2,
3, 12, 20, 42, 105}, {2, 3, 12, 20, 45, 90}, {2, 3, 12, 20, 48,
80}, {2, 3, 12, 20, 50, 75}, {2, 3, 12, 20, 55, 66}, {2, 3, 12, 21,
29, 812}, {2, 3, 12, 21, 30, 420}, {2, 3, 12, 21, 32, 224}, {2, 3,
12, 21, 35, 140}, {2, 3, 12, 21, 36, 126}, {2, 3, 12, 21, 42,
84}, {2, 3, 12, 21, 44, 77}, {2, 3, 12, 22, 27, 1188}, {2, 3, 12,
22, 28, 462}, {2, 3, 12, 22, 30, 220}, {2, 3, 12, 22, 33, 132}, {2,
3, 12, 22, 36, 99}, {2, 3, 12, 22, 44, 66}, {2, 3, 12, 24, 25,
600}, {2, 3, 12, 24, 26, 312}, {2, 3, 12, 24, 27, 216}, {2, 3, 12,
24, 28, 168}, {2, 3, 12, 24, 30, 120}, {2, 3, 12, 24, 32, 96}, {2,
3, 12, 24, 33, 88}, {2, 3, 12, 24, 36, 72}, {2, 3, 12, 24, 40,
60}, {2, 3, 12, 24, 42, 56}, {2, 3, 12, 25, 30, 100}, {2, 3, 12,
26, 39, 52}, {2, 3, 12, 27, 36, 54}, {2, 3, 12, 28, 30, 70}, {2, 3,
12, 30, 36, 45}, {2, 3, 13, 14, 56, 2184}, {2, 3, 13, 14, 78,
182}, {2, 3, 13, 14, 84, 156}, {2, 3, 13, 15, 44, 2860}, {2, 3, 13,
15, 45, 1170}, {2, 3, 13, 15, 50, 325}, {2, 3, 13, 15, 52,
260}, {2, 3, 13, 15, 60, 156}, {2, 3, 13, 15, 65, 130}, {2, 3, 13,
16, 39, 624}, {2, 3, 13, 16, 48, 156}, {2, 3, 13, 17, 34, 663}, {2,
3, 13, 18, 30, 1170}, {2, 3, 13, 18, 36, 156}, {2, 3, 13, 18, 39,
117}, {2, 3, 13, 19, 27, 13338}, {2, 3, 13, 20, 26, 780}, {2, 3,
13, 20, 30, 156}, {2, 3, 13, 21, 24, 2184}, {2, 3, 13, 21, 26,
273}, {2, 3, 13, 21, 28, 156}, {2, 3, 13, 24, 26, 104}, {2, 3, 14,
15, 36, 1260}, {2, 3, 14, 15, 40, 280}, {2, 3, 14, 15, 42,
210}, {2, 3, 14, 15, 60, 84}, {2, 3, 14, 16, 32, 672}, {2, 3, 14,
16, 35, 240}, {2, 3, 14, 16, 42, 112}, {2, 3, 14, 16, 48, 84}, {2,
3, 14, 17, 28, 1428}, {2, 3, 14, 18, 26, 819}, {2, 3, 14, 18, 27,
378}, {2, 3, 14, 18, 28, 252}, {2, 3, 14, 18, 35, 90}, {2, 3, 14,
18, 36, 84}, {2, 3, 14, 18, 42, 63}, {2, 3, 14, 19, 24, 1064}, {2,
3, 14, 20, 24, 280}, {2, 3, 14, 20, 28, 105}, {2, 3, 14, 20, 30,
84}, {2, 3, 14, 20, 35, 60}, {2, 3, 14, 21, 22, 462}, {2, 3, 14,
21, 24, 168}, {2, 3, 14, 21, 28, 84}, {2, 3, 14, 21, 30, 70}, {2,
3, 14, 24, 28, 56}, {2, 3, 14, 24, 35, 40}, {2, 3, 15, 16, 27,
2160}, {2, 3, 15, 16, 28, 560}, {2, 3, 15, 16, 30, 240}, {2, 3, 15,
16, 32, 160}, {2, 3, 15, 16, 35, 112}, {2, 3, 15, 16, 40, 80}, {2,
3, 15, 16, 48, 60}, {2, 3, 15, 17, 25, 850}, {2, 3, 15, 17, 34,
85}, {2, 3, 15, 18, 23, 1035}, {2, 3, 15, 18, 24, 360}, {2, 3, 15,
18, 25, 225}, {2, 3, 15, 18, 27, 135}, {2, 3, 15, 18, 30, 90}, {2,
3, 15, 18, 35, 63}, {2, 3, 15, 18, 36, 60}, {2, 3, 15, 20, 21,
420}, {2, 3, 15, 20, 22, 220}, {2, 3, 15, 20, 24, 120}, {2, 3, 15,
20, 25, 100}, {2, 3, 15, 20, 28, 70}, {2, 3, 15, 20, 30, 60}, {2,
3, 15, 20, 36, 45}, {2, 3, 15, 21, 28, 60}, {2, 3, 15, 21, 35,
42}, {2, 3, 15, 24, 30, 40}, {2, 3, 16, 17, 24, 272}, {2, 3, 16,
18, 21, 1008}, {2, 3, 16, 18, 24, 144}, {2, 3, 16, 18, 36, 48}, {2,
3, 16, 20, 24, 80}, {2, 3, 16, 20, 30, 48}, {2, 3, 16, 21, 28,
48}, {2, 3, 18, 20, 30, 36}, {2, 3, 18, 21, 28, 36}, {2, 3, 20, 21,
28, 30}}

1591个解。

{{2, 4, 5, 21, 421, 176820}, {2, 4, 5, 21, 422, 88620}, {2, 4, 5, 21,
423, 59220}, {2, 4, 5, 21, 424, 44520}, {2, 4, 5, 21, 425,
35700}, {2, 4, 5, 21, 426, 29820}, {2, 4, 5, 21, 427, 25620}, {2,
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4, 10, 14, 20, 35}, {2, 4, 10, 15, 16, 48}, {2, 4, 10, 15, 18,
36}, {2, 4, 10, 15, 20, 30}, {2, 4, 10, 15, 21, 28}, {2, 4, 11, 12,
14, 231}, {2, 4, 11, 12, 15, 110}, {2, 4, 11, 12, 22, 33}, {2, 4,
12, 14, 15, 35}}

586个解。

{{2, 5, 6, 8, 121, 14520}, {2, 5, 6, 8, 122, 7320}, {2, 5, 6, 8, 123,
4920}, {2, 5, 6, 8, 124, 3720}, {2, 5, 6, 8, 125, 3000}, {2, 5, 6,
8, 126, 2520}, {2, 5, 6, 8, 128, 1920}, {2, 5, 6, 8, 129,
1720}, {2, 5, 6, 8, 130, 1560}, {2, 5, 6, 8, 132, 1320}, {2, 5, 6,
8, 135, 1080}, {2, 5, 6, 8, 136, 1020}, {2, 5, 6, 8, 138, 920}, {2,
5, 6, 8, 140, 840}, {2, 5, 6, 8, 144, 720}, {2, 5, 6, 8, 145,
696}, {2, 5, 6, 8, 150, 600}, {2, 5, 6, 8, 152, 570}, {2, 5, 6, 8,
156, 520}, {2, 5, 6, 8, 160, 480}, {2, 5, 6, 8, 165, 440}, {2, 5,
6, 8, 168, 420}, {2, 5, 6, 8, 170, 408}, {2, 5, 6, 8, 180,
360}, {2, 5, 6, 8, 184, 345}, {2, 5, 6, 8, 192, 320}, {2, 5, 6, 8,
195, 312}, {2, 5, 6, 8, 200, 300}, {2, 5, 6, 8, 210, 280}, {2, 5,
6, 8, 216, 270}, {2, 5, 6, 8, 220, 264}, {2, 5, 6, 9, 46,
2070}, {2, 5, 6, 9, 48, 720}, {2, 5, 6, 9, 50, 450}, {2, 5, 6, 9,
54, 270}, {2, 5, 6, 9, 60, 180}, {2, 5, 6, 9, 70, 126}, {2, 5, 6,
9, 72, 120}, {2, 5, 6, 10, 31, 930}, {2, 5, 6, 10, 32, 480}, {2, 5,
6, 10, 33, 330}, {2, 5, 6, 10, 34, 255}, {2, 5, 6, 10, 35,
210}, {2, 5, 6, 10, 36, 180}, {2, 5, 6, 10, 39, 130}, {2, 5, 6, 10,
40, 120}, {2, 5, 6, 10, 42, 105}, {2, 5, 6, 10, 45, 90}, {2, 5, 6,
10, 48, 80}, {2, 5, 6, 10, 50, 75}, {2, 5, 6, 10, 55, 66}, {2, 5,
6, 11, 24, 1320}, {2, 5, 6, 11, 30, 110}, {2, 5, 6, 12, 21,
420}, {2, 5, 6, 12, 22, 220}, {2, 5, 6, 12, 24, 120}, {2, 5, 6, 12,
25, 100}, {2, 5, 6, 12, 28, 70}, {2, 5, 6, 12, 30, 60}, {2, 5, 6,
12, 36, 45}, {2, 5, 6, 13, 18, 1170}, {2, 5, 6, 13, 20, 156}, {2,
5, 6, 14, 20, 84}, {2, 5, 6, 14, 21, 70}, {2, 5, 6, 14, 30,
35}, {2, 5, 6, 15, 16, 240}, {2, 5, 6, 15, 18, 90}, {2, 5, 6, 15,
20, 60}, {2, 5, 6, 15, 24, 40}, {2, 5, 6, 16, 20, 48}, {2, 5, 6,
18, 20, 36}, {2, 5, 6, 20, 21, 28}, {2, 5, 7, 8, 32, 1120}, {2, 5,
7, 8, 35, 280}, {2, 5, 7, 8, 40, 140}, {2, 5, 7, 8, 42, 120}, {2,
5, 7, 8, 56, 70}, {2, 5, 7, 9, 42, 45}, {2, 5, 7, 10, 18, 630}, {2,
5, 7, 10, 20, 140}, {2, 5, 7, 10, 21, 105}, {2, 5, 7, 10, 30,
42}, {2, 5, 7, 12, 14, 420}, {2, 5, 7, 12, 15, 140}, {2, 5, 7, 12,
20, 42}, {2, 5, 7, 14, 20, 28}, {2, 5, 8, 9, 16, 720}, {2, 5, 8, 9,
18, 120}, {2, 5, 8, 9, 20, 72}, {2, 5, 8, 9, 24, 45}, {2, 5, 8,
10, 14, 280}, {2, 5, 8, 10, 15, 120}, {2, 5, 8, 10, 16, 80}, {2, 5,
8, 10, 20, 40}, {2, 5, 8, 10, 24, 30}, {2, 5, 8, 11, 12,
1320}, {2, 5, 8, 12, 15, 40}, {2, 5, 8, 12, 20, 24}, {2, 5, 9, 10,
12, 180}, {2, 5, 9, 10, 15, 45}, {2, 5, 9, 10, 18, 30}, {2, 5, 9,
12, 18, 20}, {2, 5, 10, 12, 15, 20}}
103个解。

{{2, 6, 7, 8, 16, 336}, {2, 6, 7, 8, 21, 56}, {2, 6, 7, 8, 24,
42}, {2, 6, 7, 9, 14, 126}, {2, 6, 7, 9, 18, 42}, {2, 6, 7, 10, 12,
140}, {2, 6, 7, 10, 15, 42}, {2, 6, 7, 12, 14, 28}, {2, 6, 8, 9, 12,
72}, {2, 6, 8, 9, 18, 24}, {2, 6, 8, 10, 12, 40}, {2, 6, 8, 10, 15,
24}, {2, 6, 9, 10, 15, 18}}

13个解。

{{3, 4, 5, 6, 21, 420}, {3, 4, 5, 6, 22, 220}, {3, 4, 5, 6, 24,
120}, {3, 4, 5, 6, 25, 100}, {3, 4, 5, 6, 28, 70}, {3, 4, 5, 6, 30,
60}, {3, 4, 5, 6, 36, 45}, {3, 4, 5, 7, 14, 420}, {3, 4, 5, 7, 15,
140}, {3, 4, 5, 7, 20, 42}, {3, 4, 5, 8, 11, 1320}, {3, 4, 5, 8,
12, 120}, {3, 4, 5, 8, 15, 40}, {3, 4, 5, 8, 20, 24}, {3, 4, 5, 9,
10, 180}, {3, 4, 5, 9, 12, 45}, {3, 4, 5, 9, 18, 20}, {3, 4, 5, 10,
12, 30}, {3, 4, 5, 10, 15, 20}, {3, 4, 6, 7, 10, 140}, {3, 4, 6,
7, 12, 42}, {3, 4, 6, 7, 14, 28}, {3, 4, 6, 8, 9, 72}, {3, 4, 6, 8,
10, 40}, {3, 4, 6, 8, 12, 24}, {3, 4, 6, 9, 12, 18}, {3, 4, 6, 10,
12, 15}}
27个解。

总计1591+586+103+13+27=2320个解。

葡萄糖 · 发表于 2019-9-21 09:47:38

本帖最后由葡萄糖于 2019-9-21 09:53 编辑

【强烈建议管理员改一下标题】（方便以后搜索）
比如：埃及分数互异正整数解及其组数
A006585
Egyptian fractions: number of solutions to 1 = 1/x_1 + ... + 1/x_n in positive integers x_1 < ... < x_n.
1, 0, 1, 6, 72, 2320, 245765, 151182379, ⋅⋅⋅⋅⋅⋅

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