First triangle number to have over five hundred divisors

no_of_prime_factors.py

from collections import defaultdict
from math import sqrt


def number_prime_factors(n):
	factors = defaultdict(int)	
	
	while(n % 2 == 0):
		factors[2] += 1
		n = n // 2

	for i in range(3, int(sqrt(n)) + 1, 2):
		while(n % i == 0):
			factors[i] += 1
			n = n // i

	if n > 2:
		factors[n] = 1

	total_factors = 1
	for exp in factors.values():
		total_factors *= (1 + exp)
	return total_factors


no_to_process = 100000000
_sum = 1
no_divisors_to_exceed = 500

for i in range(2, no_to_process):
	_sum += i
	no_of_divisors = number_prime_factors(_sum)
	if no_of_divisors > no_divisors_to_exceed:
		print(_sum)
		break
else:
	raise Exception('Increase no_to_process')