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projecteuler---->problem=12----Highly divisible triangular number

2024-07-06 17:32:27   339人阅读

title:

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?

翻译：

「三角数」即用递增的自然数相加得到的数，因此第7个三角数为1 + 2 + 3 + 4 + 5 + 6 + 7 = 28。前10个三角数为：

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

先让我们来看看前7个三角数各自都有哪些因数吧：

  • 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

可见，28是第一个拥有超过5个因数的三角数。

那么第一个拥有超过500个因数的三角数是……？

解答：

import time
def getCount(a):
	count=0
	b=a
	if a==1:
		return 1
	if a%2==0:
		i=2
	else :
		i=3
	while i < b:
		if a%i==0:
			count+=2
			b=a/i	
			if b==i:
				count-=1
				break		
		i+=1
	return count+2
s=0
i=1
start=time.time()
while True:
	s += i
	size=getCount(s)
	if size >= 500:
		break
	i+=1;
stop=time.time()
print "time is ",stop-start
print s



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