12.py

# 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 sympy import divisor_count


def get_nth_triangle(n: int) -> int:
    return n * (n + 1) // 2


def find_x_divisors_triangle(x: int) -> int:
    triangle_number = triangle = 1
    while True:
        if (divisor_count(triangle) > x):
            return triangle

        triangle_number += 1
        triangle = get_nth_triangle(triangle_number)


print(f"Triangle with min x divisors: {find_x_divisors_triangle(500)}")