How to resolve the algorithm Möbius function step by step in the Ring programming language

Published on 12 May 2024 09:40 PM
#Ring

How to resolve the algorithm Möbius function step by step in the Ring programming language

Table of Contents

Problem Statement

The classical Möbius function: μ(n) is an important multiplicative function in number theory and combinatorics. There are several ways to implement a Möbius function. A fairly straightforward method is to find the prime factors of a positive integer n, then define μ(n) based on the sum of the primitive factors. It has the values {−1, 0, 1} depending on the factorization of n:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Möbius function step by step in the Ring programming language

Source code in the ring programming language

mobStr = "      . "

for i = 1 to 200
    if mobius(i) >= 0
       mobStr + = " "
    ok
    temp = string(mobius(i))
    if left(temp,2) = "-0"
       temp = right(temp,len(temp)-1)
    ok
    mobStr += temp + " "
    if i % 10 = 9  
        see mobStr + nl
        mobStr = "     "
    ok
next

func mobius(n)
     if n = 1 
        return 1
     ok
     for d = 2 to ceil(sqrt(n))
         if n % d = 0  
            if n % (d*d) = 0
               return 0
            ok
            return -mobius(n/d)
         ok
     next 
     return -1

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