algorithm: mobius function implementation #1088

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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
	}

19 changes: 19 additions & 0 deletions 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)
	})
	})

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