Project Euler 12

• 問題

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?

• 解答例

import sympy

def triangleNum(num):
    return num * (num + 1) // 2

def countDivisor(num):
    if num == 1:
        return 1
    count = 1
    result = sympy.factorint(num)
    for v in result.values():
        count *= (v + 1)
    return count

n = 1
while countDivisor(triangleNum(n)) < 500:
    n += 1

print(n, triangleNum(n))