**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?

**Script**

Execution Time: 24.6897 seconds

require_once 'functions.php'; function getTriangle($n) { $a = range(0, $n); return array_sum($a); } function addOne($n) { return ++$n; } function getArrayProduct($a) { $b = 1; foreach($a as $v) { $b *= $v; } return $b; } $maxDiv = 500; $x = 1; do { $x++; $t = getTriangle($x); $xa = new primefactor($t); $c = getArrayProduct(array_map('addOne', array_count_values($xa->factor))); } while ($c < $maxDiv); echo $t.PHP_EOL;