Project Euler 第12题

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?

寻找最小的超过500个除数的三角数。
triangle numbers(三角数)：三角数通项公式为：n2/2+n/2。

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1 楼 lampeter123 2009-08-11  

import psyco,math
psyco.full()

def triNum(n):
    if(n%2==0):
        return n/2*(n+1)
    else:
        return (n+1)/2*n

def factorNum(n):
    count = 0
    for i in xrange(2,math.sqrt(n)+1):
        if n%i==0:
            count = count+2
    if n==math.sqrt(n)*math.sqrt(n):
        count = count-1
    return count

if __name__ == "__main__":
    x=2079
    while(True):
        y = triNum(x)
        print y
        if factorNum(y)>=500:
            break
        x=x+1

    print x