Problem012.java

/**
 * Problem 12:
 * The sequence of triangle numbers is generated by adding the natural numbers.
 * So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:
 * 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
 * Let us list the factors of the first seven triangle numbers:
 * 1: 1
 * 3: 1,3
 * 6: 1,2,3,6
 * 10: 1,2,5,10
 * 15: 1,3,5,15
 * 21: 1,3,7,21
 * 28: 1,2,4,7,14,28
 * We can see that 28 is the first triangle number to have over five divisors.
 * What is the value of the first triangle number to have over five hundred divisors?
 */
public class Problem012 {

    private static int firstTriangleNumberOver(int divisors) {
        int i = 1, triangle = 1;
        while (getNumberOfDivisors(triangle) < divisors) {
            i++;
            triangle += i;
        }
        return triangle;
    }

    private static int getNumberOfDivisors(int n) {
        int divisors = 2;
        for (int d=2; d*d<=n; d++) {
            if (n%d == 0) {
                divisors++;
                if (n/d != d) {
                    divisors++;
                }
            }
        }
        return divisors;
    }

    public static void main(String[] args) {
        System.out.println("The value of the first triangle number to have over five hundred divisors is:");
        System.out.println(firstTriangleNumberOver(500));
    }

}