判定梅森质数的卢卡斯序列

Treenewbee

蔡家雄 发表于 2023-11-26 12:00
6=1*6=2*3，有1/1+1/6+1/2+1/3=2，

哪个正整数的所有因子的倒数的和是等于3的？

哪个正整数的所有因子的倒数的和是等于3的？

120, 672, 523776, 459818240, 1476304896, 51001180160...

A005820

Treenewbee

哪个正整数的所有因子的倒数的和是等于4的？

30240, 32760, 2178540, 23569920, 45532800, 142990848, 1379454720, 43861478400, 66433720320, 153003540480, 403031236608, 704575228896, 181742883469056...

A027687

Treenewbee

哪个正整数的所有因子的倒数的和是等于4的？

30240, 32760, 2178540, 23569920, 45532800, 142990848, 1379454720, 43861478400, 66433720320, 153003540480, 403031236608, 704575228896, 181742883469056...

A027687

Treenewbee

穷举一定范围，找到部分结果，OEIS搜索即可：

1. Select[Range[10^7], DivisorSigma[1, #] == 3 # &]

复制代码

{120, 672, 523776}

1. Select[Range[10^7], DivisorSigma[1, #] == 4 # &]

复制代码

{30240, 32760, 2178540}

Treenewbee

A215264                Numbers k such that sigma(k) > 5*k.               

122522400, 147026880, 183783600, 205405200, 220540320, 232792560, 245044800, 273873600, 294053760, 328648320, 367567200, 410810400, 428828400, 441080640, 465585120, 490089600, 492972480, 497296800, 514594080, 537213600, 547747200, 551350800, 563603040

Treenewbee

穷举一定范围，用返回结果搜索OEIS即可

1. Select[Range[10^7], DivisorSigma[1, #] == 4 # &]
   

复制代码

{30240, 32760, 2178540}

蔡家雄

猜想：真分数 10/m=1/x+1/y+1/z 有的无解，

猜想：真分数 11/m=1/x+1/y+1/z 都有解，

11/12-1/2-1/3 = 1/12
11/13-1/2-1/3 = 1/78
11/14-1/2-1/4 = 1/28
11/15-1/2-1/5 = 1/30
11/16-1/2-1/6 = 1/48
11/17-1/2-1/7 = 1/238
11/18-1/2-1/10 = 1/90
11/19-1/2-1/13 = 1/494
11/20-1/2-1/21 = 1/420
11/21-1/2-1/43 = 1/1806
11/22-1/3-1/7 = 1/42
11/23-1/3-1/7 = 1/483
11/24-1/3-1/9 = 1/72
11/25-1/3-1/10 = 1/150
11/26-1/3-1/12 = 1/156
11/27-1/3-1/14 = 1/378
11/28-1/3-1/17 = 1/1428
11/29-1/3-1/22 = 1/1914
11/30-1/3-1/31 = 1/930
11/31-1/3-1/47 = 1/4371
11/32-1/3-1/97 = 1/9312

Treenewbee

穷举一定范围，用返回结果搜索OEIS即可

1. Select[Range[10^7], DivisorSigma[1, #] == 4 # &]
   

复制代码

{30240, 32760, 2178540}

Treenewbee

穷举一定范围，用返回结果搜索OEIS即可

1. Select[Range[10^7], DivisorSigma[1, #] == 4 # &]
   

复制代码

{30240, 32760, 2178540}

Treenewbee

穷举一定范围，用返回结果搜索OEIS即可

1. Select[Range[10^7], DivisorSigma[1, #] == 4 # &]
   

复制代码

{30240, 32760, 2178540}