Problem 55345. Easy Sequences 68: Factorial Rectangles

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>I'll celebrate my comeback to Cody with this one easy problem...</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:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The rectangle below is special:</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=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"142\"/><w:attr w:name=\"width\" w:val=\"182\"/><w:attr w:name=\"verticalAlign\" w:val=\"middle\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Its area is </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>40,320</w:t></w:r></w:customXml><w:r><w:t> which equal 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>8!</w:t></w:r></w:customXml><w:r><w:t>. We call such rectangle a </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>factorial rectangle</w:t></w:r><w:r><w:t>, which is an integer-sided rectangle with an area equal to a factorial number. </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 problem, we want to know how many are these factorial rectangles.</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 a given 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 define the function </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>C_{FR}(n)</w:t></w:r></w:customXml><w:r><w:t> as the number of factorial rectangles with area </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> The factorial rectangles with area </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>5!=120</w:t></w:r></w:customXml><w:r><w:t> are as follows: </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,\\ 120],\\ [2,\\ 60],\\ [3,\\ 40],\\ [4,\\ 30],\\ [5,\\ 24],\\ [6,\\ 20],\\ [8,\\ 15],\\ [10,\\ 12]</w:t></w:r></w:customXml><w:r><w:t>, with rotations not allowed. Hence, </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>C_{FR}(5)=8.</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>Write a function that will calculate </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>S_{FR}(n)</w:t></w:r></w:customXml><w:r><w:t>, defined as follows:</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>S_{FR}(n) = \\sum_{i=1}^n C_{FR}(i)</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>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=6</w:t></w:r></w:customXml><w:r><w:t>, we are given:</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>S_{FR}(6) = \\sum_{i=1}^5 C_{FR}(i) = C_{FR}(1)+C_{FR}(2)+C_{FR}(3)+C_{FR}(4)+C_{FR}(5)+C_{FR}(6) = 1+1+2+4+8+15 = 31.</w:t></w:r></w:customXml></w:p></w:body></w:document>","relationship":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","target":"/media/image1.jpeg","relationshipId":"rId1"}]},{"partUri":"/media/image1.jpeg","contentType":"image/jpeg","content":"data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4REARXhpZgAATU0AKgAAAAgABAE7AAIAAAASAAAISodpAAQAAAABAAAIXJydAAEAAAAkAAAQ1OocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAFJhbW9uIFZpbGxhbWFuZ2NhAAAFkAMAAgAAABQAABCqkAQAAgAAABQAABC+kpEAAgAAAAM4MgAAkpIAAgAAAAM4MgAA6hwABwAACAwAAAieAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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<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: 556px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 278px; transform-origin: 407px 278px; 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: 200.5px 8px; transform-origin: 200.5px 8px; unicode-bidi: normal; "><span style="">I'll celebrate my comeback to Cody with this one easy problem...</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: 40px 8px; transform-origin: 40px 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: 97px 8px; transform-origin: 97px 8px; unicode-bidi: normal; "><span style="">The rectangle below is special:</span></span></div><div style="block-size: 142px; font-family: 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data-image-state="image-loaded" width="182" height="142"></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; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; 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: 32.5px 8px; transform-origin: 32.5px 8px; unicode-bidi: normal; "><span style="">Its area is </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 47px; height: 18px;" width="47" 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: 49px 8px; transform-origin: 49px 8px; unicode-bidi: normal; "><span style=""> which equal to </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 15.5px; height: 18px;" width="15.5" 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: 83.5px 8px; transform-origin: 83.5px 8px; unicode-bidi: normal; "><span style="">. We call such rectangle a </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: 64px 8px; transform-origin: 64px 8px; unicode-bidi: normal; "><span style="font-weight: 700; ">factorial rectangle</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: 115.5px 8px; transform-origin: 115.5px 8px; unicode-bidi: normal; "><span style="">, which is an integer-sided rectangle with an area equal to a factorial number. </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: 230.5px 8px; transform-origin: 230.5px 8px; unicode-bidi: normal; "><span style="">In this problem, we want to know how many are these factorial rectangles.</span></span></div><div style="block-size: 65px; 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 32.5px; text-align: left; transform-origin: 384px 32.5px; 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: 62px 8px; transform-origin: 62px 8px; unicode-bidi: normal; "><span style="">For a given 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: 75px 8px; transform-origin: 75px 8px; unicode-bidi: normal; "><span style="">, we define the function </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" style="width: 44.5px; height: 20px;" width="44.5" height="20"></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: 150px 8px; transform-origin: 150px 8px; unicode-bidi: normal; "><span style=""> as the number of factorial rectangles with area </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 19.5px; height: 18px;" width="19.5" 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: 43.5px 8px; transform-origin: 43.5px 8px; unicode-bidi: normal; "><span style=""> The factorial rectangles with area </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 56.5px; height: 18px;" width="56.5" 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: 49px 8px; transform-origin: 49px 8px; unicode-bidi: normal; "><span style=""> are as follows: </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 443.5px; height: 18.5px;" width="443.5" height="18.5"></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: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; "><span style="">, with rotations not allowed. Hence, </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJUAAAAoCAYAAAD39rjkAAAHCElEQVR4Xu2by+t2UxTH3/cPQC4jSXIZyIBcSygGiJJCrslArmVCvMhAck2U5FbKgBAmilyKASnXyMDAJRNGrvkDWB+dby27vc9Z+5x9nuf3PM6p1fM85+yz99prffe67f3s3rVciwQaS2B34/6W7hYJ7FpAtYCguQQWUDUX6dLh/wFU55iafzL6qpG6r7V+nm7U11Z2s+2gusS0dprRDQ21B0hvMrrc6NeG/W5NV1NBdahJ4kAnjb8Si3CK/f5mTcIHUOcb8dl3pXPwbY+yH38avZR0QJ83G529prm1BuDR1uFeXaeT9TUGVADlsk5Z+9rn90bfdQydZZ+/G31itH9374TWEgj0B4+vGx0RUPpb1ga+cxdzKfVxqz07xKilFQxMrVkTFtMtnR4f6HplPiwY9Me8fhgzWg2oQPODTgG32fdXk4Fh9GWj4ztmnlyD0AHzt924qYVJZQT4PugRHHN8qPCccT42whW+OUb4a3wHXb7fgSd143oGe+ixGlhRUIHeJ4xkmS6w76XAV8I+zNr0KWUumWJBrjE6PDAAVuoPoyEXWepKcolYxAA7K2uCZ0E/5xYWBMnIU0ajjEIEVAjuxW66uLqTjIYCVDFVYnou6dVYKVbklz2CjfCo8W63xpuSEWrezO+YgnGQBcf97xcRhG8zBKrUPYDuiDkU4wcEAFjLc197gTkyLpb3eqNTjX4Ozis3Nv2caRSxjC3nOrYvr9PSolcbjEj1vPpApVWIy+O6rnI1rqOe82nH61ByQOyHwPzF72eM0jhxSHmy5KVVP/T+qp+j11+6QT+zz1wGe6/dv8PoPqM7axnsA5VWMn2OMoO1zExsL2FFBOHnlhu2ZgHJKte8M3Gqk1/383/bevPBugL13+w+Fjjimf7DUAlUHs28sI6Au1ZyMtlRXlWbOdkGushIGavGjYBTbf+2L2OCWuR8ZO1EM+1r3TfjkqRozhiN84z2NnreiKz5LqOh2DnLeglUik300iaYdvFMjPThCEUBykcTcEX7AlSseFxJzTVU0oj2NcZKpsBiLMB1hdGkEkkJVCD14m5Gm+D6YJVSAnW0KBBKCktdQwQorHoC2tqgVrW/KHhK7R4bCYQSsE63/kbvlZZAhT9VgE4wNxT4ThVKi/dbgQpeCPhxDX0Vdc+zqvJD2XSLebbsQzLD1ZMJS+eMMbocVBIC5lwXFfKxxcGWAhjqqyWofG0u4vo3EVSyyAIPGTH3/JbVKKsfAVVNwDqk+DmftwSVT1QioIqWMuacf03fklXOYHj337RONYf748jI3Z1bQQBkSz92kjjWPklfMb9SIoH3/d093BDtjzNC4SgxzU5kXUatroxGZK0jBd+xgfq6sj/pt+TifExdLc9IoF4qkNWsDLVVUS0Xp5EJPWfkt4HkVvyKUpaXJhC1JYU+/mWpoisVUI2x6OvI/vyYJSvst3KqM8sSqHxMgfAjLoB2KpyVNlgVAOcUgCJfMPLZllbUpXZfJw68a/L3GX9svSgFmOYfAYqUlPISWXTryP4ioJIs+WwGKjoTAPiO6xkqhukMUykd9WDwZpcAMVe19Zua/giGX0WpaQZ4uKuhbJW+0wOFHgQ6HxapKMtyRtxkBGiraJNbrH5cr6t0Xjy70Ch3ePHfPob2/jgvRKdcrNpnMwDwh7366hta/bgUryxcHFXwtC6iYDJ1lfL36fYCPGqMPgX7eAG3yh6XBzWBKv1Ei4DwzxWpZ60CMJExvGxze39aKEOBfHb3YqiuAirvMaKGwUUc847RF0b7GBE4k4JGLJmyCkB1lRFbAlcalSyLLCUTe9zooO49jfdwAgb40yY4JxlLh+skUAlfSQArj3NYWKkcyHPK0sb0GNcXUf6cbXx8e7UNpEWtBAk932iUbtX4RZkND4ZApUkhvBONDjY6o7v5uX1+bfRuZuCcMHQwzGd9e6xhDgDe/KJglA34eDcHJj9e5JCejkQzLy4O6rFQPjKq2eJhLPYNh9ztnOCY0jfzx5VJp/T13oAcZGhYjI/kdB8F1RTGebd0MKzk+ryrJBtk4pxEjGZjWLlXjErWaup8eB+F4JrZiK0BYouxd3QfqwKVfHR6chQTnDuvI1cpn+4tV6RuAohfM+o79jxVMSwIVvWcwJ3K41reXxWoVG+KHg+Rq/TprHx5dNtIpw7m+BvVpv+TZlawrQpUqk5HNim9q/RZHBX5NzppRPlWHajlHz9xza3/oDqrklfdeVQ5U/jyYIjUcpSd5eKnnAUb4o3Yhz9Kjj7KkQzAfCadNxpieNOfzw0qFMBZH9W6cnUhL0O/38f9tA6iNJhnm5jGbzpeQvzPDaoQE0uj7ZLAAqrt0ueOmM0Cqh2hhu1iYgHVdulzR8xmAdWOUMN2MbGAarv0uSNms4BqR6hhu5j4Bwm2rjiFUiB2AAAAAElFTkSuQmCC" style="width: 74.5px; height: 20px;" width="74.5" height="20"></span></div><div style="block-size: 22px; 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 11px; text-align: left; transform-origin: 384px 11px; 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: 106.5px 8px; transform-origin: 106.5px 8px; unicode-bidi: normal; "><span style="">Write a function that will calculate </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" style="width: 42px; height: 20px;" width="42" height="20"></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: 62px 8px; transform-origin: 62px 8px; unicode-bidi: normal; "><span style="">, defined as follows:</span></span></div><div style="block-size: 45px; 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 22.5px; text-align: left; transform-origin: 384px 22.5px; 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: 96px 8px; transform-origin: 96px 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: 122.5px; height: 45px;" width="122.5" height="45"></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: 13px 8px; transform-origin: 13px 8px; unicode-bidi: normal; "><span style="">For </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 36.5px; height: 18px;" width="36.5" 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: 46px 8px; transform-origin: 46px 8px; unicode-bidi: normal; "><span style="">, we are given:</span></span></div><div style="block-size: 45px; 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 22.5px; text-align: left; transform-origin: 384px 22.5px; 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: 36px 8px; transform-origin: 36px 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: 667.5px; height: 45px;" width="667.5" height="45"></span></div></div></div>

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Problem 55345. Easy Sequences 68: Factorial Rectangles

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Problem 55345. Easy Sequences 68: Factorial Rectangles

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