MobiusFunction.java

package com.thealgorithms.maths.Prime;

/*
 * Java program for mobius function
 * For any positive integer n, define μ(n) as the sum of the primitive nth roots of unity.
 * It has values in {−1, 0, 1} depending on the factorization of n into prime factors:
 *   μ(n) = +1 if n is a square-free positive integer with an even number of prime factors.
 *   μ(n) = −1 if n is a square-free positive integer with an odd number of prime factors.
 *   μ(n) = 0 if n has a squared prime factor.
 * Wikipedia: https://en.wikipedia.org/wiki/M%C3%B6bius_function
 *
 * Author: Akshay Dubey (https://github.com/itsAkshayDubey)
 *
 * */
public final class MobiusFunction {
    private MobiusFunction() {
    }

    /**
     * This method returns μ(n) of given number n
     *
     * @param number Integer value which μ(n) is to be calculated
     * @return  1 when number is less than or equals 1
     *            or number has even number of prime factors
     *          0 when number has repeated prime factor
     *         -1 when number has odd number of prime factors
     */
    public static int mobius(int number) {
        if (number <= 0) {
            // throw exception when number is less than or is zero
            throw new IllegalArgumentException("Number must be greater than zero.");
        }

        if (number == 1) {
            // return 1 if number passed is less or is 1
            return 1;
        }

        int primeFactorCount = 0;

        for (int i = 1; i <= number; i++) {
            // find prime factors of number
            if (number % i == 0 && PrimeCheck.isPrime(i)) {
                // check if number is divisible by square of prime factor
                if (number % (i * i) == 0) {
                    // if number is divisible by square of prime factor
                    return 0;
                }
                /*increment primeFactorCount by 1
                                if number is not divisible by square of found prime factor*/
                primeFactorCount++;
            }
        }

        return (primeFactorCount % 2 == 0) ? 1 : -1;
    }
}