Source Code

import java.util.*;
class smith
{
    public static void main()
    {
        Scanner sc = new Scanner(System.in);
        int sum=0,s=0,n, i=2;
        System.out.println("Enter number:");
        n=sc.nextInt();
        int n1=n;
        //sum of digits
        while(n!=0)
        {
            int d=n%10;
            s+=d;
            n/=10;
        }
        while(n1!=0)
        {
            if(n1%i==0)
                if(n1!=10)
                    sum+=i;
                else
                {
                    int sum1=0,i1=i;
                    while(i1>0)
                    {
                        sum1= i1%10;
                        i1/=10;
                        sum+=sum1;
                        n1/=i;
                    }
                }
            
            else
            {
                i++;
            }
        }
        if(sum==s)
        System.out.println("YES");
        else
        System.out.println("no");
    }
}


What is a Smith Number?

A Smith number is a special type of composite number in mathematics that exhibits a unique property involving its digits and their factorization. Named after the mathematician Albert Wilansky, who first described them in the 1980s, Smith numbers hold an intriguing characteristic.

To understand a Smith number, one must first comprehend the concept of the "digit sum" and the "prime factorization" of a number. The digit sum of a number is the sum of all its individual digits. For example, the digit sum of 123 is 1 + 2 + 3 = 6. Prime factorization involves expressing a number as the product of its prime factors. For instance, the prime factorization of 20 is 2 × 2 × 5.


Now, a number is considered a Smith number if the sum of its digits is equal to the sum of the digits of its prime factors. However, there's a catch: the prime factors must be different from the number itself. In other words, if we take the prime factors of a Smith number and sum their digits, it should be the same as the sum of the digits of the original number, excluding the prime factors themselves.




For example, let's consider the number 85. Its prime factorization is 5 × 17. The sum of the digits of 85 is 8 + 5 = 13, and the sum of the digits of its prime factors (excluding 5 and 17) is 1 + 7 = 8. Remarkably, these sums are equal, making 85 a Smith number.





Smith numbers have captured the interest of mathematicians due to their curious nature. They offer a fascinating interplay between the properties of digits and prime factorization, leading to intriguing patterns and relationships within the realm of number theory. Despite being a relatively specialized concept, Smith numbers contribute to the broader understanding of mathematical structures and properties.