/*

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?

*/

class Problem_12{

/* returns the nth triangle number; that is, the sum of all the natural numbers less than, or equal to, n */

public static int triangleNumber(int n) {

int sum = 0;

for (int i = 0; i <= n; i++)

sum += i;

return sum;

}

public static void main(String[] args) {

int j = 0;

int n = 0;

int noOfDiv = 0;

while (noOfDiv<= 500) { //checks if no of divisors<=500

noOfDiv= 0;

j++;

n = triangleNumber(j);

// checking for divisors and counting them untill sqrt(n)

for (int i = 1; i <= Math.sqrt(n); i++)

if (n % i == 0)

noOfDiv++;

// 1 to the square root of the number holds exactly half of the divisors

// so multiply it by 2 to include the other corresponding half

noOfDiv*= 2;

}

System.out.println(n);

}

}