algorithm: mobius function implementation (#1088)

* feat: Add mobius function implementation

* test: Add tests for mobius function

* fix: Code style fixes

* fix: Code style fixes

* fix: Store prime factors in a variable &  add throw error

* fix: Fix unit tests for zero and negative numbers

* fix: Minor code style fixes

Maths/MobiusFunction.js

@@ -0,0 +1,29 @@
+/*
+ * Author: Akshay Dubey (https://github.com/itsAkshayDubey)
+ * Mobius Function: https://en.wikipedia.org/wiki/M%C3%B6bius_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.
+ */
+
+/**
+ * @function mobiusFunction
+ * @description -> This method returns μ(n) of given number n
+ * returns 1 when number is less than or equals 1
+ * or number has even number of prime factors
+ * returns 0 when number has repeated prime factor
+ * returns -1 when number has odd number of prime factors
+ * @param {Integer} number
+ * @returns {Integer}
+ */
+
+import { PrimeFactors } from './PrimeFactors.js'
+export const mobiusFunction = (number) => {
+  const primeFactorsArray = PrimeFactors(number)
+  if (number <= 0) {
+    throw new Error('Number must be greater than zero.')
+  }
+  return primeFactorsArray.length !== new Set(primeFactorsArray).size ? 0 : primeFactorsArray.length % 2 === 0 ? 1 : -1
+}