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Problem 21


Problem 21


Amicable numbers

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.


亲和数

记d(n)为n的所有真因数(小于n且整除n的正整数)之和。
如果d(a) = b且d(b) = a,且a ≠ b,那么a和b构成一个亲和数对,a和b被称为亲和数。

例如,220的真因数包括1、2、4、5、10、11、20、22、44、55和110,因此d(220) = 284;而284的真因数包括1、2、4、71和142,因此d(284) = 220。

求所有小于10000的亲和数的和。