（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.

d(n)定义为n 的所有真因子（小于 n 且能整除 n 的整数）之和。 如果 d(a) = b 并且 d(b) = a, 且 a  b, 那么 a 和 b 就是一对相亲数（amicable pair），并且 a 和 b 都叫做亲和数（amicable number）。

例如220的真因子是 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 和 110; 因此 d(220) = 284. 284的真因子是1, 2, 4, 71 和142; 所以d(284) = 220.

计算10000以下所有亲和数之和。

// （Problem 21）Amicable numbers 

// Completed on Wed, 24 Jul 2013, 06:07

// Language: C

//

// 版权所有（C）acutus   (mail: [email protected]) 

// 博客地址：http://www.cnblogs.com/acutus/

#include<stdio.h>



int FactorSum(int n)  //计算n的所有小于n的因素和

{

    int i;

    int sum=1;

    for(i=2; i<=n/2; i++)

    {

        if(n%i==0)

            sum+=i;

    }

    return sum;

}



int main()

{

    int t,i=2;

    int sum=0;

    while(i<10000)

    {

        t=FactorSum(i);

        if(t!=i && FactorSum(t)==i) 

            sum+=i;

        i++;

    }

    printf("%d\n",sum);

    return 0;

}

Answer:

31626