2022-09-06 15:25:28 +05:30
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/*
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* Author: Akshay Dubey (https://github.com/itsAkshayDubey)
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* Mobius Function: https://en.wikipedia.org/wiki/M%C3%B6bius_function
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* For any positive integer n, define μ(n) as the sum of the primitive nth roots of unity.
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* It has values in {−1, 0, 1} depending on the factorization of n into prime factors:
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* μ(n) = +1 if n is a square-free positive integer with an even number of prime factors.
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* μ(n) = −1 if n is a square-free positive integer with an odd number of prime factors.
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* μ(n) = 0 if n has a squared prime factor.
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*/
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/**
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* @function mobiusFunction
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* @description -> This method returns μ(n) of given number n
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* returns 1 when number is less than or equals 1
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* or number has even number of prime factors
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* returns 0 when number has repeated prime factor
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* returns -1 when number has odd number of prime factors
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* @param {Integer} number
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* @returns {Integer}
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*/
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import { PrimeFactors } from './PrimeFactors.js'
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export const mobiusFunction = (number) => {
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const primeFactorsArray = PrimeFactors(number)
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if (number <= 0) {
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throw new Error('Number must be greater than zero.')
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}
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2023-10-03 23:08:19 +02:00
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return primeFactorsArray.length !== new Set(primeFactorsArray).size
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? 0
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: primeFactorsArray.length % 2 === 0
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? 1
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: -1
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2022-09-06 15:25:28 +05:30
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}
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