本文探讨了亲和数的概念及如何找出10000以内的所有亲和数并计算其总和。亲和数是指两个数中一个数的所有真因数之和等于另一个数的情况。例如220和284即为一对亲和数。
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
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
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