Problem 53119. Easy Sequences 53: Greatest Proper Divisor

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 greatest proper divisor (</w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>GPD</w:t></w:r></w:customXml><w:r><w:t>) of an integer </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>x</w:t></w:r></w:customXml><w:r><w:t> is the largest integer </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>y</w:t></w:r></w:customXml><w:r><w:t>, such that </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>y\\ |\\ x</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>y &lt;x</w:t></w:r></w:customXml><w:r><w:t>. Furthermore, we define: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>GPD(1)= 1</w:t></w:r></w:customXml><w:r><w:t>. </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>Below is the set of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>GPD</w:t></w:r></w:customXml><w:r><w:t>'s of numbers from </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>1</w:t></w:r></w:customXml><w:r><w:t> to </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>25</w:t></w:r></w:customXml><w:r><w:t>:</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> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\{1,\\ 1,\\ 1,\\ 2,\\ 1,\\ 3,\\ 1,\\ 4,\\ 3,\\ 5,\\ 1,\\ 6,\\ 1,\\ 7,\\ 5,\\ 8,\\ 1,\\ 9,\\ 1,\\ 10,\\ 7,\\ 11,\\ 1,\\ 12,\\ 5\\}</w:t></w:r></w:customXml><w:r><w:t>.</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>Given an integer </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, create a function that outputs the sum of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>GPD</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>'s of all integers from </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>1</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t> to </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>, inclusive</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>.</w:t></w:r><w:r><w:t> For </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n=25</w:t></w:r></w:customXml><w:r><w:t>, your function should return, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>107</w:t></w:r></w:customXml><w:r><w:t>.</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>TIP</w:t></w:r><w:r><w:t>: Good algorithms for finding GPD's for numbers </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>1</w:t></w:r></w:customXml><w:r><w:t> to </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>100</w:t></w:r></w:customXml><w:r><w:t>, can be found in </w:t></w:r><w:hyperlink w:docLocation=\"https://rosettacode.org/wiki/Largest_proper_divisor_of_n\"><w:r><w:t>Rosetta Code</w:t></w:r></w:hyperlink><w:r><w:t>.</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: 183px; 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; ">The greatest proper divisor (<img src="data:image/png;base64,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" width="34" height="18" style="width: 34px; height: 18px;"><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; ">) of an integer x<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; "> is the largest integer y<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; ">, such that <img src="data:image/png;base64,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" width="37" height="19" style="width: 37px; height: 19px;"><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; "> and <img src="data:image/png;base64,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" width="36.5" height="18" style="width: 36.5px; height: 18px;"><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; ">. Furthermore, we define: <img src="data:image/png;base64,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" width="79" height="19" style="width: 79px; height: 19px;"><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; ">. </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; ">Below is the set of <img src="data:image/png;base64,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" width="34" height="18" style="width: 34px; height: 18px;"><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; ">'s of numbers from 1<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; "> to <img src="data:image/png;base64,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" width="18" height="18" style="width: 18px; height: 18px;"><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; ">:</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; "> <img 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" width="486" height="19" style="width: 486px; height: 19px;"><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; ">.</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; ">Given an integer n<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; ">, create a function that outputs the sum of <img src="data:image/png;base64,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" width="34" height="18" style="width: 34px; height: 18px;"><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; ">'s of all integers from 1<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; "> to n<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; ">, inclusive<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="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; "> For <img src="data:image/png;base64,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" width="44" height="18" style="width: 44px; height: 18px;"><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; ">, your function should return, <img src="data:image/png;base64,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" width="25.5" height="18" style="width: 25.5px; height: 18px;"><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; ">.</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; ">TIP<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; ">: Good algorithms for finding GPD's for numbers 1<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; "> to <img src="data:image/png;base64,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" width="25.5" height="18" style="width: 25.5px; height: 18px;"><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; ">, can be found in <a target='_blank' href = "https://rosettacode.org/wiki/Largest_proper_divisor_of_n">Rosetta Code</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; ">.</div></div></div>

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Problem 53119. Easy Sequences 53: Greatest Proper Divisor

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Problem 53119. Easy Sequences 53: Greatest Proper Divisor

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