JavaScript/Maths/MobiusFunction.js at master · TheAlgorithms/JavaScript · GitHub

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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

}

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