Problem 12

Problem Statement :Problem12

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?

Algorithm:

• We  solve the problem on a basic assumption that if one factor of the number is present within root of the number the we need not iterate over all the factors till n/2.
• count can be incremented twice just because of the above reason.
• The value of  n = i * (i+1) / 2 is evident for i in the  

Solution:

public class problem12 {
 public static void main(String args[]) {
  for (int i = 10;; i++) {
   int n = i * (i + 1) / 2;
   int count = 2;
   for (int k = 2; k * k <= n; k++) {
    if (n % k == 0)
     count += 2;
   }
   if (count >= 500) {
    System.out.println(n);
    break;
   }
  }
 }
}