第12题:
What is the value of the first triangle number to have over five hundred divisors?
找出第一个拥有500个因数的1-n连续自然数之和.
分析:相邻两个自然数没有公约数,其乘积的因数数量,等于两个数各自的因数数量之积.
# -*- coding: gb2312 -*-# 找出第1个拥有500个因数的1-n的自然数之和import mathimport timedef yan( n ):
"""遍历得出n的因数个数""" s = [ x
for x
in xrange(1,
int(math.sqrt(n))+1)
if not n%x ] start = s[-1]==math.sqrt(n) and -2 or -1
for i
in s[start::-1]: s.append(n/i)
return sstart = time.time()x = 2
while 1: n2 = len(yan(x/2)) n1 = len(yan(x-1)) n3 = len(yan(x+1))
if n1*n2>500: print x,x-1,x*(x-1)/2
break if n3*n2>500: print x,x+1,x*(x+1)/2
break x+=2end = time.time()print end-start
开始我理解错误,以为是求第一个有500个因数的自然数,那结果应该是2**4*3**4*5*7,结果始终不正确.唉,英语差了真老火啊.
