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## Project Euler 12–Highly divisible triangular number

Wu Yudong    November 10, 2017     欧拉计划   614

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?

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

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

#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;
}