012.js

/*
Problem 12: Highly divisible triangular number
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 n divisors?
*/

const divisibleTriangleNumber = n => {

  const getNumberOfFactors = num => {
    const maxToCheck = ~~(Math.sqrt(num));
    const factors = [1, num];
    for (let i = 2; i <= maxToCheck; i++) {
      if (num % i === 0) {
        factors.push(i);
        factors.push(num / i);
      }
    }
    return factors.length;
  }

  // loop through triangular numbers to find the one
  let triangularNum = 1;
  let indInSequence = 1;
  while (getNumberOfFactors(triangularNum) < n) {
    indInSequence++;
    triangularNum = (indInSequence * (indInSequence + 1)) / 2;
  }
  return triangularNum;
}

console.log(divisibleTriangleNumber(500));