package Maths;

/**
 * <p>
 * In number theory, the aliquot sum s(n) of a positive integer n is the sum of all proper divisors of n,
 * that is, all divisors of n other than n itself.
 * For example, the proper divisors of 15 (that is, the positive divisors of 15 that are not equal to 15)
 * are 1, 3 and 5, so the aliquot sum of 15 is 9 i.e. (1 + 3 + 5).
 * </p>
 * Wikipedia: https://en.wikipedia.org/wiki/Aliquot_sum
 */
public class AliquotSum {
    public static void main(String[] args) {
        assert aliquotSum(1) == 0;
        assert aliquotSum(6) == 6;
        assert aliquotSum(15) == 9;
        assert aliquotSum(19) == 1;
    }

    /**
     * Finds the aliquot sum of an integer number
     *
     * @param number a positive integer
     * @return aliquot sum of given {@code number}
     */
    public static int aliquotSum(int number) {
        int sum = 0;
        for (int i = 1, limit = number / 2; i <= limit; ++i) {
            if (number % i == 0) {
                sum += i;
            }
        }
        return sum;
    }
}