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?