Problem 21 of Evaluate the sum of all the amicable numbers under 10000.

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.

public class AmicableNumbers {public static void main(String args[]){int all=0;for(int i=2;i<10000;i++){if(amicableNum(i)<10000&&amicableNum(amicableNum(i))<10000&&amicableNum(i)!=amicableNum(amicableNum(i))){if(i==amicableNum(amicableNum(i))){System.out.println("i="+i);System.out.println("amicableNumI="+amicableNum(i));System.out.println("amicableNumII="+amicableNum(amicableNum(i)));all+=i;System.out.println("inall="+all);}}}System.out.println("all="+all);}public static int amicableNum(int n){int sum=0;for(int i=n;i>1;i--){if(n%i==0){sum+=n/i;}}return sum;}}

Answer:

31626