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26 lines
980 B
JavaScript
26 lines
980 B
JavaScript
/*
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* Author: Akshay Dubey (https://github.com/itsAkshayDubey)
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* Liouville Function: https://en.wikipedia.org/wiki/Liouville_function
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* For any positive integer n, define λ(n) as the sum of the primitive nth roots of unity.
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* It has values in {−1, 1} depending on the factorization of n into prime factors:
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* λ(n) = +1 if n positive integer with an even number of prime factors.
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* λ(n) = −1 if n positive integer with an odd number of prime factors.
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*/
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/**
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* @function liouvilleFunction
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* @description -> This method returns λ(n) of given number n
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* returns 1 when number has even number of prime factors
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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} 1|-1
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*/
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import { PrimeFactors } from './PrimeFactors.js'
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export const liouvilleFunction = (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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return PrimeFactors(number).length % 2 === 0 ? 1 : -1
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}
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