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from __future__ import print_function

from math import sqrt

'''

Highly divisible triangular numbers

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?

'''

try:

xrange #Python 2

except NameError:

xrange = range #Python 3

def count_divisors(n):

nDivisors = 0

for i in xrange(1, int(sqrt(n))+1):

if n%i == 0:

nDivisors += 2

#check if n is perfect square

if n**0.5 == int(n**0.5):

nDivisors -= 1

return nDivisors

tNum = 1

i = 1

while True:

i += 1

tNum += i

if count_divisors(tNum) > 500:

break

print(tNum)

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