## Problem:

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.

31626

## Code:The solution may include methods that will be found here: Library.java .

public interface EulerSolution{

public String run();

}
/*
* Solution to Project Euler problem 21
* By Nayuki Minase
*
* http://nayuki.eigenstate.org/page/project-euler-solutions
* https://github.com/nayuki/Project-Euler-solutions
*/

public final class p021 implements EulerSolution {

public static void main(String[] args) {
System.out.println(new p021().run());
}

public String run() {
int sum = 0;
for (int i = 1; i < 10000; i++) {
if (isAmicable(i))
sum += i;
}
return Integer.toString(sum);
}

private static boolean isAmicable(int n) {
int m = divisorSum(n);
return m != n && divisorSum(m) == n;
}

private static int divisorSum(int n) {
int sum = 0;
for (int i = 1; i < n; i++) {
if (n % i == 0)
sum += i;
}
return sum;
}

}