Smith Number in Java

In this section, we will explore the concept of Smith numbers and develop Java programs to determine whether a given number is a Smith number. The topic of Smith numbers often appears in Java coding tests and academic assignments. Our focus will be on understanding the characteristics of Smith numbers and implementing code to check if a given number qualifies as a Smith number.

What is a Smith Number?

A Smith number, also known as a joke number, is a composite number that possesses the unique property of having the sum of its digits equal to the sum of the digits of its prime factors, excluding the number 1. Smith numbers can be found in the sequence OEIS A006753. In our exploration, we will delve into the characteristics of Smith numbers and develop Java programs to determine whether a given number qualifies as a Smith number.

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

Smith Number Example

Example 1: Suppose, we want to check whether the number 85 is smith or not.

The sum of digits = 8 + 5 = 13

Prime factors of 85 are 5,17

The sum of digits of its prime factors = 5 + 1+ 7 = 13

Compare the sum of digits with the sum of digits of its prime factors i.e. 13=13. Both are equal. Hence, the given number (85) is a Smith number.

Example 2: Let’s check whether another number 999 is Smith or not.

The Sum of digits = 9+ 9+9 = 27

Prime factors of 999 are: 3×3×3,37

The sum of digits of its prime factors = 3+3+3+3+7 =19

Compare the sum of digits with the sum of digits of its prime factors i.e. 27≠19. Hence, the given number (999) is not a Smith number.

Steps to Find Smith Number

Read or assign a value to the variable representing the number from the user.
Calculate the sum of the digits of the given number.
Find the prime factors of the given number.
Determine the sum of the digits of the prime factors.
Compare the sum of the digits of the given number with the sum of the digits of its prime factors.
If the sums are equal, then the given number is a Smith number.
Otherwise, it is not a Smith number.

Smith Number Program in Java

SmithNumberExample.java

import java.util.*;  
public class SmithNumberExample  
{  
//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.");  
}  
}

Output 1:

Enter a number: 265
Sum of Digits of the given number is = 13
Sum of digits of its prime factors is = 13
The given number is a smith number.

Output 2:

Enter a number: 2805
Sum of Digits of the given number is = 15
Sum of digits of its prime factors is = 18
The given number is not a smith number.

SmithNumberExample1.java

import java.util.*;  
public class SmithNumberExample1   
{  
//function finds all the prime factors for the given number  
static List<Integer> findPrimeFactors(int n)   
{  
//creating an array list that stores the prime factors      
List<Integer> result = new ArrayList<>();  
for (int i = 2; n % i == 0; n = n/i)  
result.add(i);  
for (int i = 3; i * i <= n; i =i+2)   
{  
while (n % i == 0)   
{  
result.add(i);  
n = n/i;  
}  
}  
if (n != 1)  
//the add() method adds the prime factors to the list  
result.add(n);  
return result;  
}  
//function finds the sum of digits of the given number  
static int sumOfDigits(int n)   
{  
int sum = 0;  
while (n > 0)   
{  
//finds the last digit and add it to the sum      
sum =sum+(n % 10);  
//removes the last digit from the number  
n = n/10;  
}  
//returns the sum of digits  
return sum;  
}  
//driver code      
public static void main(String args[])   
{  
//finds all smit numbers up to 10000      
for (int n = 1; n < 10000; n++)   
{  
//calling the user-defined function that finds prime factors  
List<Integer> factors = findPrimeFactors(n);  
//the size() method returns the number of elements in the list  
//executes until the condition becomes false  
if (factors.size() > 1)   
{  
int sum = sumOfDigits(n);  
for (int f : factors)  
sum =sum-sumOfDigits(f);  
if (sum == 0)  
System.out.println(n);  
}  
}  
}  
}

Output:

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