Mobius Function of number...

The MOBIUS function µ(n) for a natural number N is defined as follows:

µ(n) = 1 if n is a square free positive integer with an even number of prime factors.
µ(n) = 0 if n has a squared prime factor.
µ(n) = -1 if n is a square free positive integer with an odd number of prime factors.

Example:

µ(26)=1                ( for 26 = 2 * 13     µ(26) = ( -1)^2= 1 )

µ(19)=-1               ( for 19 = 19     µ(19) = ( -1)^1= -1 )

µ(62)=1                ( for 62 = 2 * 31     µ(61) = ( -1)^2= 1 )

µ(28)=0                ( for 28 = 2 * 2 * 7     µ(28) = 0 for 2 appears two times )

import java.util.*;

class MobiusFunction

{

    int k;

    

    MobiusFunction()   \default constructor

    {

        k = ;

    }

    

    void input()    \input value of k

    {

        Scanner sy = new Scanner(System.in);    

        System.out.print("Enter a number : ");

        k = sy.nextInt();

    }

    

    /*  The function primefac() either returns '0' if prime factors are repeated

     *  or returns the no.of prime factors */

    int primeFac()   \to check and count prime factor of k

    {

        int a=k, i=2, b=, c=, j=;

            

        while(a > 1) // loop to generate prime factors

        {

            c = ;    // variable to store frequency of every prime factor

            while(a%i == )   // if 'i' is a prime factor

            {

                c++; // counting frequency of 'i'

                j++; // counting no of prime factors

                a=a/i;

            }

                i++;

            if(c > 1) // returning '0' if prime factors are repeated

                return ;

        }

        return j; // returning no. of prime factors

    }

    

    void display() // function to calculate value of Mobius Function

    {

        int m,x;

        if(n == 1) // condition 1

            m = 1;

        else

        {

            x = primeFac();

            if(x == ) // condition 2

                m = ;

            else // condition 3

                m = (int)Math.pow(-1,x);

        }

        System.out.println("Value of Mobius Function : "+m);

    }

    

    public static void main(String args[])

    {

        MobiusFunction ob = new MobiusFunction();    

        ob.input();

        ob.display();    

    }

}

 Output:

Enter a number : 78
Value of Mobius Function : -1

Enter a number : 12
Value of Mobius Function : 0

Enter a number : 34
Value of Mobius Function : 1

Enter a number : 17
Value of Mobius Function : -1