(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: acutus@126.com) // 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:
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31626 |
作者:acutus
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