Smith_Number.java

// In this section, we will learn what is a smith number and also create Java
// programs to check if the given number is smith or not. The smith number
// program frequently asked in Java coding tests and academics.

// Smith Number
// A Smith number is a composite number whose sum of digits equals to the sum of
// digits of its prime factors, excluding 1. It is also known as a joke number.
// It is a sequence of OEIS A006753.

// Sum of digits of n = Sum of digits of prime factors of n (counted with
// multiplicity)

import java.util.*;

public class Smith_Number {
    // function finds the sum of digits of its prime factors
    static int findSumPrimeFactors(int n) {
        int i = 2, sum = 0;
        while (n > 1) {
            if (n % i == 0) {
                sum = sum + findSumOfDigit(i);
                n = n / i;
            } else {
                do {
                    i++;
                } while (!isPrime(i));
            }
        }
        // returns the sum of digits of prime factors
        return sum;
    }

    // function finds the sum of digits of the given numbers
    static int findSumOfDigit(int n) {
        // stores the sum
        int s = 0;
        while (n > 0) {
            // finds the last digit of the number and add it to the variable s
            s = s + n % 10;
            // removes the last digit from the given number
            n = n / 10;
        }
        // returns the sum of digits of the number
        return s;
    }

    // function checks if the factor is prime or not
    static boolean isPrime(int k) {
        boolean b = true;
        int d = 2;
        while (d < Math.sqrt(k)) {
            if (k % d == 0) {
                b = false;
            }
            d++;
        }
        return b;
    }

    // driver code
    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);
        System.out.print("Enter a number: ");
        // reads an integer from the user
        int n = sc.nextInt();
        // calling the user-defined function that finds the sum of digits of the given
        // number
        int a = findSumOfDigit(n);
        // calling the user-defined function that finds the sum of prime factors
        int b = findSumPrimeFactors(n);
        System.out.println("Sum of Digits of the given number is = " + a);
        System.out.println("Sum of digits of its prime factors is = " + b);
        // compare both the sums
        if (a == b)
            // prints if above condition returns true
            System.out.print("The given number is a smith number.");
        // prints if above condition returns false
        else
            System.out.print("The given number is not a smith number.");
    }
}