algorithm: mobius function implementation (TheAlgorithms#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

Author: itsAkshayDubey

Maths/MobiusFunction.js

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+/*
+ * 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
+}

Maths/test/MobiusFunction.test.js

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+import { mobiusFunction } from '../MobiusFunction'
+
+const expectedValuesArray = [1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, 0, 1, 1, -1, 0, 0, 1, 0, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, 1, 1, 0, -1, -1, -1, 0, 0, 1, -1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 1, 1, -1, 0, -1, 1, 0, 0, 1, -1, -1, 0, 1, -1, -1, 0, -1, 1, 0, 0, 1, -1, -1, 0, 0, 1, -1, 0, 1, 1, 1, 0, -1, 0, 1, 0, 1, 1, 1, 0, -1, 0, 0, 0]
+
+describe('Testing mobius function', () => {
+  for (let i = 1; i <= 100; i++) {
+    it('Testing for number = ' + i + ', should return ' + expectedValuesArray[i], () => {
+      expect(mobiusFunction(i)).toBe(expectedValuesArray[i - 1])
+    })
+  }
+
+  it('should throw error when supplied negative numbers', () => {
+    expect(() => { mobiusFunction(-1) }).toThrow(Error)
+  })
+
+  it('should throw error when supplied zero', () => {
+    expect(() => { mobiusFunction(0) }).toThrow(Error)
+  })
+})