//PerfectNumbers.java
//perfect: sum of proper divisors equals the number.
// An even perfect number is of form: 2^(k-1)*(2^k - 1) 
//   where 2^k - 1 is prime (ie. a Mersenne prime).
//   If k composite, then 2^k - 1 is not prime   eg. k=8  2^8 - 1 =63
//   but if k prime, then maybe 2^k - 1 is prime     but k=11  2^11 - 1 =2047=23*89


// No oddperfect number ever found...smallest must be bigger than 10^300 etc


import java.awt.*;
import javax.swing.*;

public class PerfectNumbers  {   

    public static void main (String[] args) {
        String input;
        int maxTry;
        long n, sum, p, q;
        int numFactors;

        input = JOptionPane.showInputDialog("Max value of k","16");
        maxTry = Integer.parseInt(input);

        for (int k=2; k<=maxTry; k++) {
	    //n = (long)(Math.pow(2,k-1)*(Math.pow(2,k)-1));
	    p = 1L<<(k-1);       //2^k-1
	    q = (1L<<k) - 1;     //2^k - 1    may be a Mersenne prime or not
	    n = p * q;
	    int A[] = new int[1000];     //how many factors can a number have???
	    numFactors = allFactors(n,A);
            System.out.print(""+k+" "+n+" ["+p+","+q+(isPrime(q)?"*":"")+"]  (#"+numFactors+")");
	    sum = 0;
	    for (int i=0; i<numFactors; i++)
	    	sum += A[i];
	    System.out.print("="+sum+" ");
	    for (int i=0; i<numFactors; i++)
	    	System.out.print(" "+A[i]);
	    System.out.println();

        }
    }
    
    static int allFactors(long n, int A[]) {
    	int count = 0;
    	A[count++] = 1;
    	//brute force
    	for (int i=2; i<=n/2; i++)
    	    if (n%i == 0)
    	    	A[count++] = i;
    	    	
    	return count;
    }
    
    static boolean isPrime(long q) {
    	for (int i=2; i<=(int)Math.sqrt(q); i++)
    	    if (q%i == 0)
    	    	return false;
    	return true;
    }
}