Add mobius function (#3241)

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

@@ -0,0 +1,57 @@
+package com.thealgorithms.maths;
+
+/*
+ * 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 class 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
+	 */
+	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;
+	}
+
+}