# 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?
"""

import math

from utils.triangular_numbers import triangulars


def divisors(number):
    """
    Get all divisors of the number.
    """
    result = [1, number]
    d = 2
    while d <= math.sqrt(number):
        if number % d == 0:
            result.append(d)
            result.append(number // d)
        d += 1
    return set(result)


def highly_divisible_triangular(divisors_count=5):
    sequence = triangulars(100000)
    for i in sequence:
        if len(divisors(i)) > divisors_count:
            return i
    return None


if __name__ == "__main__":
    print(__doc__)
    print("*" * 55)
    print(highly_divisible_triangular(500))
