Problem 12:Highly divisible triangular number
2014-04-30 10:26
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题目描述:
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?
代码:
import math
def countDivision(num):
count=0
for i in range(1,int(math.sqrt(num+1))):
if(num%i==0):
count+=1
return count*2
def cal(num):
return num*(num+1)/2
i=1
while(i>0):
temp=cal(i)
if(countDivision(temp)>=500):
print temp
break
i+=1
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?
代码:
import math
def countDivision(num):
count=0
for i in range(1,int(math.sqrt(num+1))):
if(num%i==0):
count+=1
return count*2
def cal(num):
return num*(num+1)/2
i=1
while(i>0):
temp=cal(i)
if(countDivision(temp)>=500):
print temp
break
i+=1
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