# 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?

from collections import Counter
from functools import reduce
import util

target = 76576500


for i in range(1, 100000):
    result = reduce(lambda x,y: x + y, list(range(1, i + 1)))
    # divisers = find_divisers(result)
    factors = util.find_prime_factors(result)

    total_count = 1

    for factor, count in Counter(factors).items():
        total_count *= count + 1

    if (total_count >= 500):
        # print(i)
        # print(total_count)
        print(result)
        print(result == target)
        break