##
**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.

##
**Solution:**

31626

##
**Code:**

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

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; } }

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