import java.util.ArrayList;
import java.util.List;

public class WeirdNumbers {

    public static void main(String[] args) {
        int n = 2;
        //  n += 2 : No odd weird numbers < 10^21
        for ( int count = 1 ; count <= 25 ; n += 2 ) {
            if ( isWeird(n) ) {
                System.out.printf("w(%d) = %d%n", count, n);
                count++;
            }
        }
    }

    private static boolean isWeird(int n) {
        List<Integer> properDivisors = getProperDivisors(n);
        return isAbundant(properDivisors, n) && ! isSemiPerfect(properDivisors, n);
    }

    private static boolean isAbundant(List<Integer> divisors, int n) {
        int divisorSum = divisors.stream().mapToInt(i -> i.intValue()).sum();
        return divisorSum > n;
    }

    //  Use Dynamic Programming
    private static boolean isSemiPerfect(List<Integer> divisors, int sum) {
        int size = divisors.size();

        //  The value of subset[i][j] will be true if there is a subset of divisors[0..j-1] with sum equal to i
        boolean subset[][] = new boolean[sum+1][size+1];

        // If sum is 0, then answer is true
        for (int i = 0; i <= size; i++) {
            subset[0][i] = true;
        }

        //  If sum is not 0 and set is empty, then answer is false
        for (int i = 1; i <= sum; i++) {
            subset[i][0] = false;
        }

        // Fill the subset table in bottom up manner
        for ( int i = 1 ; i <= sum ; i++ ) {
            for ( int j = 1 ; j <= size ; j++ ) {
                subset[i][j] = subset[i][j-1];
                int test = divisors.get(j-1);
                if ( i >= test ) {
                    subset[i][j] = subset[i][j] || subset[i - test][j-1];
                }
            }
        }

        return subset[sum][size];
    }

    private static final List<Integer> getProperDivisors(int number) {
        List<Integer> divisors = new ArrayList<Integer>();
        long sqrt = (long) Math.sqrt(number);
        for ( int i = 1 ; i <= sqrt ; i++ ) {
            if ( number % i == 0 ) {
                divisors.add(i);
                int div = number / i;
                if ( div != i && div != number ) {
                    divisors.add(div);
                }
            }
        }
        return divisors;
    }

}