problem 12

/*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?
*/

#include<iostream>
#include<vector>
#include<math.h>

using namespace std;

int  tri(long n){
 int counter = 0;

 for ( int i = 1; i <= ceil(pow(n, .5)); i++){
    if( n % i == 0 ) {
       counter += 2;
    }
 }     
 return counter;
}

int main(){
 vector<int> num;
 num.push_back(0);

  for ( int i = 1; i < 1000000; i++){
    int  m = i + num[i - 1];
    num.push_back(m);

     int f = tri(m);
    if(f >= 500){
     cout<< m <<endl;
     break;
     }
     
  }
  return 0;
}