problem-012.py

"""
Problem 12 - Highly Divisible Triangular Number

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?
"""


def triangle_number(n: int) -> int:
    """
    Parameters
        n (int): which triangle number to calculate
    Returns
        triangle_number (int): nth triangle number
    """

    triangle_number = sum([i for i in range(1, n + 1)])
    return triangle_number


def num_of_divisors(n: int) -> int:
    """
    Parameters
        n (int): number to find divisors for
    Returns
        divisors (int): number of divisors
    """

    divisors = 0
    perfect_square = False

    for i in range(1, round(n ** 0.5) + 1):
        if i ** 2 == n:
            perfect_square = True
        if n % i == 0:
            divisors += 1
    if perfect_square:
        return 2 * divisors - 1
    else:
        return 2 * divisors


def triangle_n_divisors(n: int) -> int:
    """
    Parameters
        n (int): number of divisors needed
    Returns
        triangle_number_n: first triangle number with n divisors
    """

    counter = 1

    while True:
        triangle_number_n = triangle_number(counter)
        if num_of_divisors(triangle_number_n) > 500:
            break
        counter += 1
    return triangle_number_n


if __name__ == "__main__":
    print(
        "The first triangle number with over 500 divisors is: "
        + str(triangle_n_divisors(500))
    )