Project Euler 第21题

Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).
If d(a) = b and d(b) = a, where a  b, then a and b are an amicable pair and each of a and b are called amicable numbers.

For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.

Evaluate the sum of all the amicable numbers under 10000.

amicable numbers中文翻译为亲和数，如果两个数a和b，a的所有真因数之和等于b,b的所有真因数之和等于a,则称a,b是一对亲和数。

举例：220的真因数为：1, 2, 4, 5, 10, 11, 20, 22, 44, 55 和 110，他们之和为284；284的真因数为：1, 2, 4, 71 和142，他们之和为220，故220和284为亲和数。

此题求10000以内亲和数之和