Program To Find Mobius Function

MobiusNumber.java

/*
A MOBIUS function M(N) returns the value -1 or 0 or 1 fora natural number (N) by
the following conditions are defined :

When,
M(N) =1         if N=1.
M(N) =0         if any prime factor of N is contained more than once.

M(N) =(-1)^P    if N is the product of ‘P’ distinct prime factors.

Write a program to accept a positive natural number (N) and display the MOBIUS result
with proper message.

Design your program which will enable the output in the format given below:

Sample 1
    INPUT: 78
    OUTPUT: 78 =2x3x13
    NUMBER OF DISTINCT PRIME FACTORS = 3
    M(78) = -1
Sample 2
    INPUT: 34
    OUTPUT: 34 =2x17
    NUMBER OF DISTINCT PRIME FACTORS = 2
    M(34) =1
Sample 3
    INPUT: 12
    OUTPUT: 12 =2x2x3
    DUPLICATE PRIME FACTORS
    M(12) = 0
Sample 4
    INPUT: 1
    OUTPUT: 1=1
    NO PRIME FACTORS
    M(1) =1
*/

import java.util.*;

class MobiusNumber {

    int Mobius(int n) {
        if (n == 1)
            return 1;

        else {
            boolean duplicate = false;

            int N = n;

            for (int i = 2; i < n; i++) {
                int count = 0;

                while (n % i == 0) {
                    count++;
                    n = n / i;
                }

                if (count > 1) {
                    duplicate = true;
                    return 0;
                }
            }

            if (duplicate == false)
                return MobiusNotDuplicate(N);

            return -2;
        }
    }

    int MobiusNotDuplicate(int n) {
        int count = 0;

        int N = n;

        for (int i = 2; i < N; i++) {
            if (n % i == 0) {
                count++;
                n /= i;
            }
        }

        return (int) Math.pow(-1, count);
    }

    public static void main() {
        Scanner sc = new Scanner(System.in);

        System.out.println("Enter the number");
        int number = sc.nextInt();

        MobiusNumber m = new MobiusNumber();
        int result = m.Mobius(number);

        System.out.println("The mobius number is " + result);
    }
}