12.js

// Highly divisible triangular number
// 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?

var firstTriangleNumberToHaveOverNDivisors = function (n) {
    var t = 0, i = 0, divisors = [];
    while (divisors.length < n) {
        t += ++i;
        divisors = [];
        for (var d = 1, l = Math.sqrt(t); d <= l; d++) {
            if (t % d == 0) {
                divisors.push(d);
                if (t / d != d) {
                    divisors.push(t / d);
                }
            }
        }
    }
    divisors.sort(function (a, b) {
        return a - b;
    });
    console.log(divisors);
    console.log(t);
};

firstTriangleNumberToHaveOverNDivisors(5);
firstTriangleNumberToHaveOverNDivisors(500);