Turkish Project Euler Question 12 Highly Divisible Triangular Number

Turkish Project Euler Question 12 Highly Divisible Triangular Number

Triangular number sequences are generated by summing consecutive natural numbers. For example, the 7th triangular number is 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first 10 triangular numbers are as follows:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, …

Now, let's list the divisors of the first 7 triangular 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

Here we see that 28 is the first triangular number to have more than 5 divisors.
So, what is the first triangular number to have over 500 divisors?