Task: Zumkeller numbers





Java: import java.util.ArrayList;
import java.util.Collections;
import java.util.List;

public class ZumkellerNumbers {

    public static void main(String[] args) {
        int n = 1;
        System.out.printf("First 220 Zumkeller numbers:%n");
        for ( int count = 1 ; count <= 220 ; n += 1 ) {
            if ( isZumkeller(n) ) {
                System.out.printf("%3d  ", n);
                if ( count % 20 == 0 ) {
                    System.out.printf("%n");
                }
                count++;
            }
        }
        
        n = 1;
        System.out.printf("%nFirst 40 odd Zumkeller numbers:%n");
        for ( int count = 1 ; count <= 40 ; n += 2 ) {
            if ( isZumkeller(n) ) {
                System.out.printf("%6d", n);
                if ( count % 10 == 0 ) {
                    System.out.printf("%n");
                }
                count++;
            }
        }
        
        n = 1;
        System.out.printf("%nFirst 40 odd Zumkeller numbers that do not end in a 5:%n");
        for ( int count = 1 ; count <= 40 ; n += 2 ) {
            if ( n % 5 != 0 && isZumkeller(n) ) {
                System.out.printf("%8d", n);
                if ( count % 10 == 0 ) {
                    System.out.printf("%n");
                }
                count++;
            }
        }

    }
    
    private static boolean isZumkeller(int n) {
        
        if ( n % 18 == 6 || n % 18 == 12 ) {
            return true;
        }
        
        List<Integer> divisors = getDivisors(n);        
        int divisorSum = divisors.stream().mapToInt(i -> i.intValue()).sum();
        
        
        if ( divisorSum % 2 == 1 ) {
            return false;
        }
        
        
        int abundance = divisorSum - 2 * n;
        if ( n % 2 == 1 && abundance > 0 && abundance % 2 == 0 ) {
            return true;
        }
        
        Collections.sort(divisors);
        int j = divisors.size() - 1;
        int sum = divisorSum/2;
        
        
        if ( divisors.get(j) > sum ) {
            return false;
        }
        
        return canPartition(j, divisors, sum, new int[2]);
    }
    
    private static boolean canPartition(int j, List<Integer> divisors, int sum, int[] buckets) {
        if ( j < 0 ) {
            return true;
        }
        for ( int i = 0 ; i < 2 ; i++ ) {
            if ( buckets[i] + divisors.get(j) <= sum ) {
                buckets[i] += divisors.get(j);
                if ( canPartition(j-1, divisors, sum, buckets) ) {
                    return true;
                }
                buckets[i] -= divisors.get(j);
            }
            if( buckets[i] == 0 ) {
                break;
            }
        }
        return false;
    }
    
    private static final List<Integer> getDivisors(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 ) {
                    divisors.add(div);
                }
            }
        }
        return divisors;
    }

}



Python: from sympy import divisors

from sympy.combinatorics.subsets import Subset

def isZumkeller(n):
    d = divisors(n)
    s = sum(d)
    if not s % 2 and max(d) <= s/2:
        for x in range(1, 2**len(d)):
            if sum(Subset.unrank_binary(x, d).subset) == s/2:
                return True

    return False



def printZumkellers(N, oddonly=False):
    nprinted = 0
    for n in range(1, 10**5):
        if (oddonly == False or n % 2) and isZumkeller(n):
            print(f'{n:>8}', end='')
            nprinted += 1
            if nprinted % 10 == 0:
                print()
            if nprinted >= N:
                return


print("220 Zumkeller numbers:")
printZumkellers(220)
print("\n\n40 odd Zumkeller numbers:")
printZumkellers(40, True)