Problem 52684. Easy Sequences 17: Mu Variant Function

Created by Ramon Villamangca

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Möbius_function\"><w:r><w:t>mobius function </w:t></w:r></w:hyperlink><w:r><w:t>is an important arithmetic function. It is often represented by the Greek letter mu (μ), and is sometimes called the \"mu function\".</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>In this excercise, we are concerned with a simplified variant of  the mobius function called 'muVar'. For a given positive integer 'n', 'muVar(n)' is defined as:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>equal to 2, if 'n' </w:t></w:r><w:r><w:rPr><w:u/></w:rPr><w:t>has</w:t></w:r><w:r><w:t> at least 1 perfect square divisor greater than 1; or</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>equal to 1, otherwise.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For example, the values of muVar for 1, 10, 20, 30 and 100 are 1, 1, 2, 1 and 2, respectively. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Our task is to create the function 'muVarSum(n)'</w:t></w:r><w:r><w:t>, which is the sum of the outputs of 'muVar' function applied from 1 to n.</w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; "><div style="block-size: 214px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; "><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">The </span></span><a target='_blank' href = "https://en.wikipedia.org/wiki/M%C3%B6bius_function"><span style=""><span style="">mobius function </span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">is an important arithmetic function. It is often represented by the Greek letter mu (μ), and is sometimes called the "mu function".</span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">In this excercise, we are concerned with a simplified variant of  the mobius function called 'muVar'. For a given positive integer 'n', 'muVar(n)' is defined as:</span></span></div><ul style="block-size: 40px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; margin-top: 10px; margin-bottom: 20px; "><li style="block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; text-align: left; white-space: pre-wrap; margin-left: 56px; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; "><span style="">equal to 2, if 'n' </span></span><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; "><span style="text-decoration: underline; text-decoration-line: underline; ">has</span></span><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; "><span style=""> at least 1 perfect square divisor greater than 1; or</span></span></li><li style="block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; text-align: left; white-space: pre-wrap; margin-left: 56px; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; "><span style="">equal to 1, otherwise.</span></span></li></ul><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">For example, the values of muVar for 1, 10, 20, 30 and 100 are 1, 1, 2, 1 and 2, respectively. </span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-weight: bold; ">Our task is to create the function 'muVarSum(n)'</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">, which is the sum of the outputs of 'muVar' function applied from 1 to n.</span></span></div></div></div>

Solve

Solution Stats

7 Solutions
2 Solvers

Last Solution submitted on Jul 30, 2022

Last 200 Solutions

Solution Comments

Solution 6513739

1 Comment

1 Comment

Ramon Villamangca on 13 Sep 2021

Hi, your logic is correct but 'nchoosek' hogs memory space. there is a better way...

Problem Recent Solvers2

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 52684. Easy Sequences 17: Mu Variant Function

Solution Stats

Last 200 Solutions

Solution Comments

Problem Recent Solvers2

Suggested Problems

More from this Author71

Problem Tags

Community Treasure Hunt

Problem 52684. Easy Sequences 17: Mu Variant Function

Solution Stats

Last 200 Solutions

Solution Comments

Problem Recent Solvers2

Suggested Problems

More from this Author71

Problem Tags

Community Treasure Hunt

Players