Zachary Stence

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?

#include<iostream>
#include<math.h>
using namespace std;

int factors(unsigned long long num) {
  int count = 0;
  for (unsigned long long i = 1; i < sqrt(num); i++) {
    if (num % i == 0) {
      count +=2;
    }
  }
  return count;
}

int triangle(int num) {
  int sum = 0;
  for (int i = num; i > 0; i--) {
    sum += i;
  }
  return sum;
}

int main () {
  unsigned long long i = 0;
  while (factors(triangle(i)) < 500) {
    i++;
  }
  cout << triangle(i) << endl;
}

Answer: 76576500