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?
public class Problem12 { static long result = 0; public static void solve() { long currentnumber = 0; long factors = 0; long sqrt = 0; for (long i = 0; i < Long.MAX_VALUE; i++) { currentnumber +=i; sqrt = (long)(Math.sqrt(currentnumber)); for (int j = 1; j < sqrt; j++) { if (currentnumber % j == 0) { factors+=2; } } if (sqrt*sqrt == currentnumber) { factors--; } System.out.println(currentnumber + " has " + factors + " factors"); if (factors >500) { result = currentnumber; return; } factors = 0; } } public static void main(String[] args) { solve(); System.out.println(result); } }
Lösung: 76576500