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 returns the value of the first triangle number to have over five hundred divisors solution 76576500 returns the value of the first triangle number to have over five hundred divisors solution 76576500
def triangle_number_generator():
    for n in range(1, 1000000):
        yield n * (n + 1) // 2


def count_divisors(n):
    divisors_count = 1
    i = 2
    while i * i <= n:
        multiplicity = 0
        while n % i == 0:
            n //= i
            multiplicity += 1
        divisors_count *= multiplicity + 1
        i += 1
    if n > 1:
        divisors_count *= 2
    return divisors_count


def solution():
    
    return next(i for i in triangle_number_generator() if count_divisors(i) > 500)


if __name__ == "__main__":
    print(solution())