# -*- coding: utf-8 -*-
"""
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?
"""

from time import time
start = time()



maxm = 0
x = 0
dhk = 0

while maxm <= 501:
	# maak het volgende driehoeksgetal
	x += 1
	dhk += x

	# test door hoeveel getallen je ieder driehoeksgetal kan delen
	teller = 0
	
	# bereken het laagste getal dat je wil testen. Begin bij x omdat de 
	# wortel van x kwadraat (x dus) altijd hoger is dan de wortel van x driehoek
	y = x
	while dhk < y*y:
		y -= 1

	for i in range(1, int(y + 1)):
		if dhk % i == 0:
			teller += 2
			if i*i == dhk:
				teller -= 1

	if teller > maxm:
		maxm = teller
		print dhk, maxm, x


print '\nTijd: ', time() - start
# Tijd: 10.0940001011
