Problem 53125. Easy Sequences 54: Product of Products of Proper Divisors

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>A divisor of a number that is less than the number is called a \"proper divisor\". </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>F</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>or a given positive 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:t>, we are asked to evaluate the following summation:</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=\"true\"/></w:customXmlPr><w:r><w:t>\\prod_{i=2}^{n}\\left (\\prod_{\\ d|i\\ \\&amp;\\  d&lt;i}^{}d\\   \\right )</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>This is equivalent to finding </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>the product of the products of proper divisors 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>2</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>.</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 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 = 10</w:t></w:r></w:customXml><w:r><w:t>, we have:</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=\"true\"/></w:customXmlPr><w:r><w:t>\\prod_{i=2}^{10}\\prod_{d|i\\ \\&amp;\\  d&lt;i}^{}d\\ = \\prod_{d|2\\ \\&amp;\\  d&lt;2}^{}d \\ \\times\\prod_{d|3\\ \\&amp;\\  d&lt;3}^{}d \\ \\times\\prod_{d|4\\ \\&amp;\\  d&lt;4}^{}d  \\ \\times\\prod_{d|5\\ \\&amp;\\  d&lt;5}^{}d\\ \\times\\prod_{d|6\\ \\&amp;\\  d&lt;6}^{}d \\ \\\\\n\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\times\\prod_{d|7\\ \\&amp;\\  d&lt;7}^{}d \\ \\times\\prod_{d|8\\ \\&amp;\\  d&lt;8}^{}d \\ \\times\\prod_{d|9\\ \\&amp;\\  d&lt;9}^{}d \\ \\times\\prod_{d|10\\ \\&amp;\\  d&lt;10}^{}d \\\\ \\\\\n\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ =1\\times1\\times(1\\cdot2)\\times1\\times(1\\cdot2\\cdot3)\\times1\\times(1\\cdot2\\cdot4)\\times(1\\cdot3)\\times(1\\cdot2\\cdot5) \\\\ \\\\\n\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ =1\\times1\\times2\\times1\\times6\\times1\\times8\\times3\\times10 \\\\ \\\\\n\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ =2880\n</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Please present your output modulo </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>1000003</w:t></w:r></w:customXml><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: 20.4333px; 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: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 413.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 206.75px; transform-origin: 407px 206.75px; vertical-align: baseline; "><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; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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; perspective-origin: 244.5px 8px; transform-origin: 244.5px 8px; unicode-bidi: normal; "><span style="">A divisor of a number that is less than the number is called a "proper divisor". </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; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; "><span style="">F</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; perspective-origin: 95.5px 8px; transform-origin: 95.5px 8px; unicode-bidi: normal; "><span style="font-weight: 700; ">or a given positive integer </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">n</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; perspective-origin: 162px 8px; transform-origin: 162px 8px; unicode-bidi: normal; "><span style="">, we are asked to evaluate the following summation:</span></span></div><div style="block-size: 45.5px; 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; perspective-origin: 384px 22.75px; text-align: left; transform-origin: 384px 22.75px; 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; perspective-origin: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; "><span style="">            </span></span><span style="vertical-align:-17px"><img src="data:image/png;base64,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" style="width: 110px; height: 45.5px;" width="110" height="45.5"></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; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; "><span style=""> </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; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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; perspective-origin: 88px 8px; transform-origin: 88px 8px; unicode-bidi: normal; "><span style="">This is equivalent to finding </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; perspective-origin: 233px 8px; transform-origin: 233px 8px; unicode-bidi: normal; "><span style="font-weight: 700; ">the product of the products of proper divisors of all integers from </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);">2</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; perspective-origin: 11px 8px; transform-origin: 11px 8px; unicode-bidi: normal; "><span style="font-weight: 700; "> to </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">n</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; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; "><span style="">.</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; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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; perspective-origin: 51.5px 8px; transform-origin: 51.5px 8px; unicode-bidi: normal; "><span style="">For example for </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 44px; height: 18px;" width="44" height="18"></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; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; "><span style="">, we have:</span></span></div><div style="block-size: 209px; 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; perspective-origin: 384px 104.5px; text-align: left; transform-origin: 384px 104.5px; 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; perspective-origin: 56px 8px; transform-origin: 56px 8px; unicode-bidi: normal; "><span style="">                            </span></span><span style="vertical-align:-99px"><img src="data:image/png;base64,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" style="width: 509px; height: 209px;" width="509" height="209"></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; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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; perspective-origin: 112.5px 8px; transform-origin: 112.5px 8px; unicode-bidi: normal; "><span style="">Please present your output modulo </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 55.5px; height: 18px;" width="55.5" height="18"></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; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; "><span style="">.</span></span></div></div></div>

Solve

Solution Stats

11 Solutions
2 Solvers

Last Solution submitted on Jan 24, 2023

Last 200 Solutions

Problem Comments

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 53125. Easy Sequences 54: Product of Products of Proper Divisors

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers2

Suggested Problems

More from this Author102

Problem Tags

Community Treasure Hunt

Problem 53125. Easy Sequences 54: Product of Products of Proper Divisors

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers2

Suggested Problems

More from this Author102

Problem Tags

Community Treasure Hunt

Players