能不能把40个完全数都写下来?最长的完全数有多少位?它的规律是什么?

Question

能不能把40个完全数都写下来?最长的完全数有多少位?它的规律是什么?

Answer 1

n取下列值时,(2^n-1)*2^(n-1)是前40个完全数：
2,3,5,7,13,17,19,31,61,89,107,127,521,607,1279,2203,2281,3217,4253,4423,9689,9941,11213,19937,21701,23209,44497,86243,110503,132049,216091,756839,859433,1257787,1398269,2976221,3021377,6972593,13466917,20996011；
前几个完全数比较短小,可以写下来：
1:6
2:28
3:496
4:8128
5:33550336
6:8589869056
7:137438691328
8:2305843008139952128
9:2658455991569831744654692615953842176
10:191561942608236107294793378084303638130997321548169216
11:13164036458569648337239753460458722910223472318386943117783728128
12:14474011154664524427946373126085988481573677491474835889066354349131199152128
第13个完全数有314位,就不写出来了