LiouvilleLambdaFunction.java

package com.thealgorithms.maths.Prime;

/*
 * Java program for liouville lambda function
 * For any positive integer n, define λ(n) as the sum of the primitive nth roots of unity.
 * It has values in {−1, 1} depending on the factorization of n into prime factors:
 *   λ(n) = +1 if n is a positive integer with an even number of prime factors.
 *   λ(n) = −1 if n is a positive integer with an odd number of prime factors.
 * Wikipedia: https://en.wikipedia.org/wiki/Liouville_function
 *
 * Author: Akshay Dubey (https://github.com/itsAkshayDubey)
 *
 * */

public final class LiouvilleLambdaFunction {
    private LiouvilleLambdaFunction() {
    }

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

        // return 1 if size of prime factor list is even, -1 otherwise
        return PrimeFactorization.pfactors(number).size() % 2 == 0 ? 1 : -1;
    }
}