求33554432的所有因數之和!!~

由於 33554432 = 2 ^ (25), 33554432的所有因數 是 1, 2, 4, 8, ....33554432.

設33554432所有因數之和是 S,
S = 1+2 + 4 +8 + .... 33554432
= 1 + 2 + 2^2 + 2^3 + ... + 2^24 + 2^25 ------------------ (1)

把 (1) 每個項乘2, 得
2S = 2 + 2^2 + 2^3 + ....+ 2^25 + 2^26 -------------(2)

(2) - (1), 2S - S = 2^26 -1
S = 2^26 -1 = 6710 8864 -1 = 6710 8863.

所以 33554432所有因數之和是6710 8863.