Project Euler Problem 12: Highly divisible triangular number

Highly divisible triangular number

Problem 12

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?

C++:

#include <iostream>
#include <cmath>

using namespace std;

const int FIVE_HUNDRED = 500;

int count(int sum)
{
    if(sum == 1)
        return 1;

    int ans = 0, end;
    end = sqrt(sum);
    for(int i=1; i<end; i++)
        if(sum % i == 0)
            ans++;
    ans <<= 1;      // ans = ans * 2;
    if(end * end == sum)
        ans++;

    return ans;
}

int main()
{
    for(int i=1, sum=1; ; ) {
        if(count(sum) > FIVE_HUNDRED) {
            cout << sum << endl;
            break;
        }
        sum += ++i;
    }

    return 0;
}

C++:

#include <iostream>

using namespace std;

//#define DEBUG

const int FIVE_HUNDRED = 500;

int count(int sum)
{
    if(sum == 1)
        return 1;

    int ans = 0;
    for(int i=1, end=sum/2; i<end; i++)
        if(sum % i == 0) {
            ans += 2;
            if(i * i == sum)
                ans--;
            end = sum / i;
        }

    return ans;
}

int main()
{
    for(int i=1, sum=1; ; ) {
#ifdef DEBUG
        cout << sum << " " << count(sum) << endl;
#endif
        if(count(sum) > FIVE_HUNDRED) {
            cout << sum << endl;

            break;
        }

        sum += ++i;
    }

    return 0;
}