Statement

The sequence of triangle numbers is generated by adding the natural numbers. So the 7^(th) 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?

Solution

For this I used a brute-force technique using the formula to get the triangle numbers(the same to
add the natural numbers from 1 to x).

from CommonFunctions import factors
 
if __name__ == '__main__':
    i = 5
    triangle = i * (i + 1) // 2
    divisors = factors(triangle)
    while len(divisors) <= 500:
        i += 1
        triangle = i * (i + 1) // 2
        divisors = factors(triangle)
    print("The result is:", triangle)

The Python file is available for download here.