ProjectEuler_P12
Problem:
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?
思路:
穷举,依次测试
C Code:
#include <stdio.h> #include <math.h> int DivisorCount(int n) { int mid = (int)sqrt(n); int i = 0,count = 0; for(i = 1;i < mid ;i++) { if(0 == n%i) { count += 2; } } if(n == i*i) { count++; } else if(0 == n%i) { count += 2; } return count; } void main() { int i = 1; for(i = 1;;i++) { int mul = i*(i+1)/2; if(500 <= DivisorCount(mul)) { printf("%d %d\n",i,mul); break; } } }
Result:
76576500