Problem 12

Solution to Problem 12. Written in Python.

Problem: 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 problems.euler_lib import euler_lib as lib

sieve = lib.eratosthenes_sieve(100000)
triangle_numbers = [1]
i = 2
ptr = 0
end = 1000000

while i < end:
    triangle_numbers.append(triangle_numbers[ptr] + i)
    ptr = ptr + 1
    i = i + 1

for i in triangle_numbers:
    if lib.divisor_count_with_sieve(i, sieve) > 500:
        print i
        break