IncPlusPlus/bigtoolbox-math

package io.github.incplusplus.bigtoolbox.math.misc;

public class AmicableMath
{
    /**
     * a and b are an amicable pair if d(a) = b and d(b) = a, where a ≠ b
     * Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).
     * @param a
     * @param b
     * @return true if a and b are an amicable pair
     */
    public static boolean amicablePair(int a, int b)
    {
        return DivisorMath.sumProperDivisors(a) == b
                && DivisorMath.sumProperDivisors(b) == a
                && a != b;
    }

    /**
     *
     * @param a the number to make an amicable pair with
     * @return a number that makes an amicable pair when paired with a. If none exists, returns 0
     */
    public static int findAmicableNumber(int a)
    {
        int possibleAmicableHalf = DivisorMath.sumProperDivisors(a);
        return amicablePair(a, possibleAmicableHalf) ? possibleAmicableHalf : 0;
    }

    /**
     *
     * @param a the number to make an amicable pair with
     * @param limit the number the other half of the pair can be no greater than
     * @return a number that makes an amicable pair when paired with a.. If none exists or the number found is greater than the limit, returns 0
     */
    public static int findAmicableNumber(int a, int limit)
    {
        int possiblePair = findAmicableNumber(a);
        return possiblePair < limit ? possiblePair : 0;
    }
    public static int sumOfAmicableNumbersUnder(int limit)
    {
        int upperBound = limit + 1;
        int[] arrayOfAmicables = new int[upperBound];
        int sumOfAmicables = 0;
        int temporaryAmicableHalf;
        for(int i = 0; i < upperBound; i++)
        {
            temporaryAmicableHalf = findAmicableNumber(i, upperBound);
            if(temporaryAmicableHalf > 0)
            {
                arrayOfAmicables[i] = i;
                arrayOfAmicables[temporaryAmicableHalf] = temporaryAmicableHalf;
                System.out.println("Added pair " + i + " and " + temporaryAmicableHalf);
            }
            i = temporaryAmicableHalf != 0 ? temporaryAmicableHalf : i; //This makes the assumption that it is safe to have the iterator skip to the other half of the amicable pair
        }
        for(int i : arrayOfAmicables)
        {
            sumOfAmicables += i;
        }
        return sumOfAmicables;
    }
}