"""
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?
"""
from math import sqrt
def count_divisors(n):
nDivisors = 0
for i in range(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
def solution():
"""Returns the value of the first triangle number to have over five hundred
divisors.
# The code below has been commented due to slow execution affecting Travis.
# >>> solution()
# 76576500
"""
tNum = 1
i = 1
while True:
i += 1
tNum += i
if count_divisors(tNum) > 500:
break
return tNum
if __name__ == "__main__":
print(solution())