Problem 12 - Highly Divisible Triangular Number

The sequence of triangle numbers is generated by adding the natural numbers. So the 7^th 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?
_________________________________________________________________________________

def trg(n):
 return n*(n+1)/2

def fac(n):
 i=2
 j=1
 while i<= n/2:
  if n%i==0:
   j=j+1
  i=i+1
 return j+1
   
def fact(n):
 if n%2==0:
  return fac(n/2)*fac(n+1)
 else:
  return fac(n)*fac((n+1)/2)

i=1
while fact(i)<500:
 i=i+1

print i, trg(i), fact(i)