Highly divisible triangular number

我的那个暴力求解，太耗时间了。

用了网上产的什么因式分解，质因数之类的。确实快！还是数学基础不行，只能知道大约。

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?

from math import sqrt
import time
def natSum(n):
    x = 1
    count = 0
    sum = 0
    while count <= n:
        sum += x
        count = 0
        for i in range(1,int(sqrt(sum))+1):
            if sum % i == 0:
                count += 2
        if sqrt(sum)==int(sqrt(sum)):
                count -= 1
        print x,sum,count,n

        x += 1

natSum(500)
'''
start=time.time()
now=2
num=1
t = 0
while t <= 500 :
    num=num+now
    now+=1
    t=0
    for x in range(1,int(sqrt(num))+1):
        if num%x==0:
            t+=2
    if sqrt(num)==int(sqrt(num)):
        t=t-1

    print num
print num
print time.time()-start
'''