project_euler/#12.py at master · robinarthur/project_euler · GitHub

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# Poblem 12
# 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?
#______________________________________________________________________________
"""
project euler #12
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 time
from math import sqrt

def count_divisors(n):
    d = {}
    count = 1

    while n % 2 == 0:
        n = n / 2
        try:
            d[2] += 1
        except KeyError:
            d[2] = 1

    for i in range(3, int(sqrt(n+1)), 2):
        while n % i == 0 and i != n:
            n = n / i
            try:
                d[i] += 1
            except KeyError:
                d[i] = 1

    d[n] = 1

    for _,v in d.items():
        count = count * (v +1)

    return count


def tri_number(num):
    next = 1 + int(sqrt(1+(8 * num)))
    return num + (next/2)


def main():
    i = 1
    while count_divisors(i) < 500:
        i = tri_number(i)
    return i


start = time.time()
answer = main()
elapsed = (time.time() - start)

print("result %s returned in %s seconds." % (answer, elapsed))