some programs on smith numbers
Answers
Answer:
A Smith number is a composite number, the sum of whose digits is the sum of the digits of its prime factors obtained as a result of prime factorization (excluding 1). The first few such numbers are 4, 22, 27, 58, 85, 94, 121
import java.util.*;
public class SmithNumbers
{
int sumDigit(int n)
{
int s=0;
while(n>0)
{
s=s+n%10;
n=n/10;
}
return s;
}
int sumPrimeFact(int n)
{
int i=2, sum=0;
while(n>1)
{
if(n%i==0)
{
sum=sum+sumDigit(i);
n=n/i;
}
else
{
do{
i++;
}while(!IsPrime(i));
}
}
return sum;
}
boolean IsPrime(int k)
{
boolean b=true;
int d=2;
while(d<Math.sqrt(k))
{
if(k%d==0)
{
b=false;
}
d++;
}
return b;
}
public static void main(String args[])
{
Scanner sc=new Scanner(System.in);
SmithNumbers ob=new SmithNumbers();
System.out.print("Enter a Number : ");
int n=sc.nextInt();
int a=ob.sumDigit(n);
int b=ob.sumPrimeFact(n);
System.out.println("Sum of Digit = "+a);
System.out.println("Sum of Prime Factor = "+b);
if(a==b)
System.out.print("It is a Smith Number");
else
System.out.print("It is Not a Smith Number");
}
}
Output:
Enter a Number : 85
Sum of Digit = 13
Sum of Prime Factor = 13
It is a Smith Number
import java.io.*;
class Smith
{
static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
//function for finding sum of digits
int sumDig(int n)
{
int s=0;
while(n>0)
{
s=s+n%10;
n=n/10;
}
return s;
}
//function for generating prime factors and finding their sum
int sumPrimeFact(int n)
{
int i=2, sum=0;
while(n>1)
{
if(n%i==0)
{
sum=sum+sumDig(i); //Here 'i' is the prime factor of 'n' and we are finding its sum
n=n/i;
}
else
i++;
}
return sum;
}
public static void main(String args[]) throws IOException
{
Smith ob=new Smith();
System.out.print("Enter a Number : ");
int n=Integer.parseInt(br.readLine());
int a=ob.sumDig(n);// finding sum of digit
int b=ob.sumPrimeFact(n); //finding sum of prime factors
System.out.println("Sum of Digit = "+a);
System.out.println("Sum of Prime Factor = "+b);
if(a==b)
System.out.print("It is a Smith Number");
else
System.out.print("It is Not a Smith Number");
}
}
Hope this helps,
ira.