Wu Yudong's Blog

The sequence of triangle numbers is generated by adding the natural numbers. So the 7^th 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?

三角形数序列是由对自然数的连加构造而成的。所以第七个三角形数是1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. 那么三角形数序列中的前十个是：

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

下面我们列出前七个三角形数的约数：

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

可以看出28是第一个拥有超过5个约数的三角形数。

那么第一个拥有超过500个约数的三角形数是多少？

#include <stdio.h> 
#include <stdbool.h>

int trinumber(int n)
{
    if(n % 2 == 0) {
        return (n / 2) * (n + 1);
    } else {
        return ((n + 1) / 2) * n;
    }
}

bool divnum(int n)
{
    int i, sum = 0;
    for(i = 1; i * i < n; i++) {
        if(n % i == 0) {
            sum += 2;
        }
    }
    if(i * i == n) sum++;
    if(sum > 500) return true;
    else return false;
}

void solve(void)
{
    int i, num;
    num = 0;
    for(i = 1; ; i++) {
        if(divnum(trinumber(i))) {
            printf("%d\n",trinumber(i));
            break;
        }
    }
}

int main(void)
{
    solve();
    return 0;
}

 Answer:76576500
Completed on Sun, 17 Nov 2013, 12:53