Add Liouville lambda function (#3284)

src/main/java/com/thealgorithms/maths/LiouvilleLambdaFunction.java

@@ -0,0 +1,34 @@
+package com.thealgorithms.maths;
+
+/*
+ * 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 class 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
+	 */
+	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;
+	}
+}