euler_problem_12.py

# Highly divisible triangular number
# 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?

import math

def numberOfFactors(val):
	numFactors = 0
	lim = math.sqrt(val)
	i = 1
	while i <= lim:
		if val % i == 0:
			numFactors += 1
		i += 1
	return 2*numFactors


listTriangleNums = [1]
idx = 1
numOfFactors = 0
while numOfFactors < 500:
	idx += 1
	newTriangleNum = reduce(lambda x, y: x+y, range(1,(idx+1)))
	listTriangleNums.append(newTriangleNum)
	numOfFactors = numberOfFactors(listTriangleNums[-1])

print listTriangleNums[-1]