PerfectNumbers.java

public class PerfectNumbers {

    /**
    *   Program:    PerfectNumbers.java
    *   Creator:    Chris Clarke
    *   Created:    31.05.2009
    *   Purpose:    Calculate series of perfect numbers.
    *           A perfect number means the sum of its factors add up to the number itself,
    *           e.g. 6 = 1+2+3
    *           The first four are: 6, 28, 496, 8128.  Find some more.
    *           Formula: 2^(n-1) * (2^n - 1) where n is prime - but not every prime!!
    *   Modified:   13.12.2014: New improved algorithm runs in an instant.
    */

    public static boolean isPrime(int n) {
        int factors = 1;    // the number itself
        int sqrt = (int) (Math.sqrt(n));

        //find factors up to square root of the number
        for (int j=1; j<=sqrt; j++)
            if (n%j==0)
                if (++factors>2)
                    return false;

        //definition of prime: 2 divisors (itself and 1)
        if (factors==2)
            return true;
        return false;

    }//end isPrime()

    public static void main(String[] args) {
        for (int n=2; n<32; n++) {
            if (!isPrime(n)) continue;

            System.out.print("n="+n+"\t");
            System.out.print("2^"+(n-1)+" * (2^"+n+" - 1) \t");

            double i = Math.pow(2, n-1) * (Math.pow(2, n)-1);
            double sqr = Math.sqrt(i);
            double j;
            double sum = 1;

            for (j=2; j<=sqr; j++)
                if (i%j==0) {
                    sum+=j;
                    sum+=i/j;
                } // if i

            if (sum==i)
                System.out.println((long)i+" is a perfect number");
            else
                System.out.println("(number is NOT perfect)");
        }//end for n
    }//end main()

}//end class PerfectNumbers