Problem 53109. Easy Sequences 52: Non-squarable 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>Any integer-sided rectangle can be cut into unit rectangles (</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\\times1</w:t></w:r></w:customXml><w:r><w:t>) and rearranged into sets of smaller rectangles. For example the </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>3\\times5</w:t></w:r></w:customXml><w:r><w:t> rectangle can be broken 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=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"75\"/><w:attr w:name=\"width\" w:val=\"246\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><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>We call an integer rectangle as \"squarable\" if it can be can be broken (i.e. cut into unit rectangles and rearranged) into any number of </w:t></w:r><w:r><w:rPr><w:u/></w:rPr><w:t>non-unit squares of equal sizes</w:t></w:r><w:r><w:t>. For example the </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>4\\times6</w:t></w:r></w:customXml><w:r><w:t> rectangle can be broken into six </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\\times2</w:t></w:r></w:customXml><w:r><w:t> squares. Therefore, the </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>4\\times6</w:t></w:r></w:customXml><w:r><w:t> rectangle is squarable.</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=\"83\"/><w:attr w:name=\"width\" w:val=\"293\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId2\"/></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>Integer rectangles that are not squarable are called \"non-squarable\". The </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>3\\times5</w:t></w:r></w:customXml><w:r><w:t> rectangle, shown in the first example above, is a non-squarable rectangle. The complete set of non-squarable 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>\\le20</w:t></w:r></w:customXml><w:r><w:t> square units are 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:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>\\{ 1\\times1,\\ 1\\times2,\\ 1\\times3,\\ 1\\times5,\\ 1\\times6,\\ 1\\times7,\\ 1\\times10,\\ 1\\times11,\\ 1\\times13,\\ 1\\times14,\\ 1\\times15,\\ 1\\times17,\\ 1\\times19,\\ 2\\times3,\\ 2\\times5,\\ 2\\times7,\\ 3\\times5\\}</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:rPr><w:b/></w:rPr><w:t>Create a program that calculates the total area of all non-squarable integer rectangles whose areas are less than or equal to a given area limit </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>A</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><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: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>A=20</w:t></w:r></w:customXml><w:r><w:t>, the program should output:</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>Total\\ Area = 1+2+3+5+6+7+10+11+13+14+15+17+19+6+10+14+15=168\\ sq.\\ units.</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:rPr><w:b/></w:rPr><w:t>NOTE:</w:t></w:r><w:r><w:t> Reflections and rotations are not significant and should be counted only 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","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: 544px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 272px; transform-origin: 407px 272px; 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; 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: 188.5px 8px; transform-origin: 188.5px 8px; unicode-bidi: normal; "><span style="">Any integer-sided rectangle can be cut into unit rectangles (</span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEUAAAAkCAYAAADfJffWAAABK0lEQVRoge2YUQ2DMBBAnwcc1AA+UFAHc1AHWEDDJMzDLEzDLGwfhaxkhNBysN5yL2n4uvZ4NL0rYBiGYRi144Dm10nsoJWczAED8JKe+CQ88ACuEpM1fGRMQ5OUjihjyn23lA4I4/OOPik9cBmHmJSUgD4pKdVKaYEncefl4Mc4V7guVCwlPZu2ivFJTF+4LlQsBfLESAmByqXANjGSQkCBFFgXIy0ElEiBZTFHCAFFUmAupucYIaBMCnx3zNJCQKGUtOPMKdc5qJKSniHpHUVajBopS4dqSYO3BRVS1qrMEWKql7Kl7EqLqVpKTh8iKUZcimN+CIbCeUoaMwkx6Qd9sO+2jSMmf1sYA7GU5jC9YG4fUhrniTtjKf9ARf+F/MlxhmEYhmEYf8Ub9AbIMJOfOosAAAAASUVORK5CYII=" style="width: 34.5px; height: 18px;" width="34.5" 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: 167px 8px; transform-origin: 167px 8px; unicode-bidi: normal; "><span style="">) and rearranged into sets of smaller rectangles. For example the </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 34.5px; height: 18px;" width="34.5" 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: 113.5px 8px; transform-origin: 113.5px 8px; unicode-bidi: normal; "><span style=""> rectangle can be broken as follows:</span></span></div><div style="block-size: 80.5px; 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 40.25px; text-align: left; transform-origin: 384px 40.25px; 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: 108px 8px; transform-origin: 108px 8px; unicode-bidi: normal; "><span style="">                                                      </span></span><img class="imageNode" style="vertical-align: baseline;width: 246px;height: 75px" 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" data-image-state="image-loaded" width="246" height="75"></div><div style="block-size: 63px; 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 31.5px; text-align: left; transform-origin: 384px 31.5px; 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: 375.5px 8px; transform-origin: 375.5px 8px; unicode-bidi: normal; "><span style="">We call an integer rectangle as "squarable" if it can be can be broken (i.e. cut into unit rectangles and rearranged) into any number of </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: 98.5px 8px; transform-origin: 98.5px 8px; unicode-bidi: normal; "><span style="text-decoration: underline; text-decoration-line: underline; ">non-unit squares of equal sizes</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: 57px 8px; transform-origin: 57px 8px; unicode-bidi: normal; "><span style="">. For example the </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 34.5px; height: 18px;" width="34.5" 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: 104.5px 8px; transform-origin: 104.5px 8px; unicode-bidi: normal; "><span style=""> rectangle can be broken into six </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 34.5px; height: 18px;" width="34.5" 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: 31.5px 8px; transform-origin: 31.5px 8px; unicode-bidi: normal; "><span style=""> squares. Therefore, the </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 34.5px; height: 18px;" width="34.5" 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: 74px 8px; transform-origin: 74px 8px; unicode-bidi: normal; "><span style=""> rectangle is squarable.</span></span></div><div style="block-size: 88.5px; 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 44.25px; text-align: left; transform-origin: 384px 44.25px; 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><img class="imageNode" style="vertical-align: baseline;width: 293px;height: 83px" 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" data-image-state="image-loaded" width="293" height="83"></div><div style="block-size: 63px; 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 31.5px; text-align: left; transform-origin: 384px 31.5px; 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: 233.5px 8px; transform-origin: 233.5px 8px; unicode-bidi: normal; "><span style="">Integer rectangles that are not squarable are called "non-squarable". The </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 34.5px; height: 18px;" width="34.5" 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: 118.5px 8px; transform-origin: 118.5px 8px; unicode-bidi: normal; "><span style=""> rectangle, shown in the first example above, is a non-squarable rectangle. The complete set of non-squarable rectangles with area </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 32.5px; height: 18px;" width="32.5" 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: 65px 8px; transform-origin: 65px 8px; unicode-bidi: normal; "><span style=""> square units are as follows:</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="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAABgwAAAAlCAYAAACeY8JaAAATDUlEQVR4nO2d63HrOgyEtwd34AbSQCpIBe7gdOAO0kJqSAnuIS2khrSQ80PGGFb0oCSQAKT9ZjT3zollS7sUHwBJAYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIas4AXgDcAVwcb4WQgghhBBCCCGEEEIIIYR0XNDF7t/QxfKrcQLwAeD3/t83AC81f5AQQgghhBBCCCGEEEIIIcWc0cXudSzfPHFwAvB1/wGuKiCEEEIIIYQQQgghhBBCYnNBF9P/sv7if3hkI9ZyRuUlEJWJtpoio55nAK/3I9q1Z9TzhIee0cio5+vE8el4XUCn5dn5GrYiW9l9AniHb52aRc+pMtk/PO8ni55jrCmLL+h0j9Y3OKIXFufW4IheRO3jHdELjfS/I3A0L9i3rEfJWEPa6pLDuw3x/v0trBn3RdFdiBynKEHKepRnOrOeU/XGB3w0zqZn9Lo3chxtjq3l8xMVFgJc7196XXHuGY/lD1EahCVcAHzDv1MnZNTzDZ2Gv73jBv9GLauesuJHH+/wb0Ay6gl0FWxfT32sqfssON1/+wdd4jYbUh5+0NUB/+BbRjPpecZ0mewfbw7XmEnPIV7RtUM/hZ/X9/t+//8burLtob/maF5YnVuDo3nxgsfgI1of72heDHG+n+/9fBzRC/Yt67BkrDE0/hw73itd7xzRYg1LWDruO6HT+RtdGbze/1/GCB5EjlPMIVuG/+D52r/hFwjNrCfQadrXs38fLcmqZ9S6N3IcrQSL8rkltm/6pfqdB3JkCiD2H07vRjyrnu+YriB+4FPZZdVTlhHd0D2P0unyasSErHoKN4yX0W/4lFEZzMl1ZBvUXfC4/giNcDY95+rOfj3aWt9sempe8PzMlwSA9NaM/eSABEu9gg1H88Li3FoczYsXPBLCEvzRAzGPukk4mhdjyPd4Ph9H9YJ9S1uWjjXeMK7/0NE6wBot1rCENeO+M7r24Rt/2wXpR90G/laTqHGKEqRfqiex9JP3rct0Zj0FiXtGqCey6hm17o0aR1uCRfkMkTCQrSf6GZwsAcR3dB0o2YrJuxHPqqfMrNFLY054zKSQ+zDfQ2uGzHqOzWTVnTaPDm9GPQUpp1Gu94yuDrrg2ddMgzp93d7vvcmop8wemEu0SIdsy3aBS8mop+YfHvWVBE1KAkAyCBvqC+jZHi1XGhzVi63n1uCIXki5H7pHGZSZD0gKOKIXY+iBpcfzcWQv2Le0Zc1Y44b5WbgnPBI4LYkWa1jC2nGffHaoTdD9qFZtRtQ4RSk3DL+8VBL5rQOg2fUEpvs1rcmsZ8S6N2ocbQlW5TNEwmDo3EidpiVEa8Qz6fmF8UBWfzmN171k0vOG8WvU25d4NnKZ9BQ+EbOxBZ6Xs0fovJSgy4DXjOsxsuh5QVmbIx0cr+1wsug5RunMW32fY1qLF0Mz51pwFC+sz63BUby4Yvr+ZEDr2X8+ihdDyL1LstP7+TiaF+xb1qNkrHFGWXssyU3P/mq0WMMSSsd9l4LP6aBdi35UhjjFGHPvQBEtW9b7mfUU/iHOrP2sekatezPE0eawKp+7TBhIpnRpUES2xNgiarRGPIueL5ivLPQyK6+HM4ueklGeYi6g1YIsegrSQHwgZkbZYlDXUk99vREHyln0LH1pmexL7bXlRxY9xygNAOmA29jv6cGwRx1s4YUsb1/aeV/roYYJg2cyeDF3b/I9noG4o3jR54TnbaIiPB9H8uIIfUtPL0oTBiXaS/vu6dPWWEN0L4CyxGXLlWm14hStvHjDdP9XfGk1FqsZ9/nA8q2q1vrwfT/P+8XCmfWMWPfWjKNlLJ+7TBjojHOpibrR2TJY2WPCoIWeb5ivvCLMcMmi5xwyOPGa3Spk07O//6Y8694vMBUsnpGWeuolklE01GTTcwrZjshzv8XsepYEgGTJrNSvY7yoz7XcIkqw8GKNrv2l72vbHyYMnsnqhUbaA8+Zb0f14hOPtmFPCYMsXhyhb+nphdVqZmnfPSdeANtjDRm8KNnSS5fL2nGXWnEKTy80Uge1iq/U0nONNvqdY98oryO0d3J83f+9df2wBz3nvjNC3SusjaNlLZ+7TBgAy4IKlsGZVg1XKdn11OiKzmtmx170lPvwHoxk0lMvPxs6vuC/JNEqqdZCT/2CIx1YfYX/TA0hk56l1+D5jojsepYEgJYMYIfKfyusvFiir+UglwmDv2T0QhANvLelO6IXsr+x9F/2lDAA4ntxpL6llxdWYw25fo8kv8Yi1hDdC/nM1PNzLvxcK9bGKby8EGS7mtYvkJ5jrZ5LNNoS3NaT3vrHz8JrbkF0PaeIUvcKW+JoGcvnbhMGQFlQwTo4Y9GIW5Jdz6Hv9pwVvwc9ZWsO72QBkE/PE7oKVl4Cp/cDlArYc2BnuQqntp6ytFDqy6EZdrKMzotMes4h2xGxfK6nJAC05IWEuqy3btMsvSjR2XqQy4TBMNm80NfT+mXHQxzNizP+9gf3ljAA4ntxpL6lhxdWYw3pt3qPn6xiDZG9KO0f6WfEmy1xCg8vgEdA8tPo+yzZomeJVhbB7Vd09cE7hgO03nWFJoOeY0SpewGbOFq28lklYbBlJqP1S1Cnggo1gjNWjbgV2fUc+m3PQWVmPV/wHKS1eGv6VjLrCXSVub4Hqfi9sN62q6ae/QHxFY/VBdfe3/fykl6v+jPCdkRAfj1LAkC6PliSMGi9DYu1F1N61xjkMmEwThYvzvjbfr4bXdNajubF0EsS95gwAOJ7odl737K1FxZjjUhbYljGGqJ6cVOfmxoD6DGtN1vjFC29kD3a9VjrBv/VTJqtek5pVnMmvNY0Qn0hZNRTvjuCltZxtEzlUybDma3wkNkqa021DiACw0GFWsEZy0bcgux6CrJcbg977vdpoec7uspoKLvouQVAVj376Er/F36z4mu856OGnnqf9zHv+5p6PPdZ9Cz9Tc/tiID8ei5NGJS+5NWy/iulhhdDutcIOABMGMwR3YvL/TwZEPUDo5lfzN4nqhdXdPr3f3uvCQMgrhdj7Llv2dILi7FGpC0xrGMNEb0oWa0ZaUsiqzhFCy9e8XhvTb/99V7NJFjpOaRdzeA2et//ixirJzPrGaHurRVHy1I+pfyYJG3e8CiMa2+uRgAReA4qvMPG5CGsG/GtZNdTkPvw3g9uD3qe8Zwh9QhWCXvQU9B78nt1Dmq9GNxaT32dXxOf07/loWkWPeeIsB0RkF/PpQmDuTKrO2x7SBgAz4NdvbWGdRCYCYN5MngBDM+m9lr9eBQv5D6H6p09JwyAeF7Msee+ZSsvLMYakbbEqBFriObFCc/BuSHddd9vaizRAss4RSsv9O/pxGSEGJalnv2gbM1grCATqOU3vcmsZ6S6F7CPo2Upny/3a/rGSi/6FdsWagUQgb97ZNcIzkSqbIH8egLddf/Cf3YssA89Be9gLLAvPYFH59br+a81qANs9Sx9Maz+nEeHK4ueU0TZjgjIrye3JCpD9wlrDXKZMCgjuhcaHRj1qq+O4IUE4sbub+8JAyCOF6XsuW/ZwoutY40oW2IItWIN0byQAJW+niu6/t0PnoN2nrOPa8QpWnih0QFE73JeQ8/+aq2awVhBxiXebWlmPaPVvRrLOFqm8qlXJq0qU294ZB6irTAAnpe3/aJOpupICYMWesrAxnPbHE12PTV6Wxiv8ronPYFH47HHQZ2lntJ5WRJU9ehwZdFziijbEQH59SwJAJUmw4D9lm39fP/CL3lT49waHNmLPjKzysubI3jxiU7n15FDDyL1v7fmCF6Usue+ZQsvto41ImyJoak1dovohey1/4Humfq8f8cZzwE7r9nHteIULbzoo/X02nmglp79FSsttj6USRCefc3sekarezWWcbQM5XPzCgNNxHcYAM+Z2rklblvwDsD2yayn7LEVJVkA5NZzCBnQ7C1h4KWn3I9Xw9Zi2biVnrpRLPncnoKqrcqn3nPQezsiIL+eJQEgvaduacLAYyl9LS/0LBnthcf2UDXOrcGRvejjPbv9CF78rjj21P5G8qKUvfYtW3mxdawhXkbZEqNGrCGLF4L0b+V6PWYf14pTtPKij37OPRIGtfTUe7bLmKhFUFb0/K74G1PsQc9odW8fizhahvJp+g4DQWanrOlU1AggDr1AZuhFiRYcIWHQQs+IyQIgr55jSEXntV/w3vSU2Rles7lbvZjOQs/SmaSliYUaZNJz6rcibEcE5NezNAD0XfA5rYVHO1fDi6GXdw35YwETBtNk8aKP9An2NJM6mhe3maM/y01m9bbmCF6Usse+ZUsvtow1ZBJApC0xrGMNWbwY+x6P56JFsqC2F33kOffoG7UIbssOKLVe6N1HZnB7JHr3oGfEurfP1jhalvIpdZBpeZJKfM1+TtYBxKlKtkZQYe8Jg1Z6llRyHtnGrHqO8Q3f2cfU0xbrQV1NPfUWMmN66dnaewiqti6fsr9rhO2IgPx6lgaAdL02VrZ1+feYyWXtxVQHt8ZglwmDcTJ50UeeW6/ZZPTCf5WHQC8e7K1v2dqLLWMNaasjbYlhGWvI5IWwZFvTWtSIU7T2ok+VoGAhNfQcCsYKLYKynv2ZPegZse7ts6VtzlQ+t8T2q3ypZQCxpHK1DiqUNmAndA/CFXWDBRn1lH0K565FVyDUczkyABj6ber5lzM6zcYqbfn9sXrvcv9bzY6D5aCutp5677+x79cvwew3xtRzGq1vSUeGes5TGgDSS+XH6gPpJA71FbJ5UdKxtR7stkoY0It5rAKj8txMXTe9mKZVwoBezFPqxdH6lh5ebBlrSFtdMvHi9f5bF9SdEWsVLM/mBfC81/dUIK2mF2viFHN4eNFHVpgN+ZJNz6lgrLAlKHtCp8nchLex+6Ke80Sse/u/ufZZjF4+++w2YbCkUrUMKpQ24vo3LYKlY2TTU859R3ftQ4d85nXgPOrZIe8Ske/vVzJSCY1VQNTzGT2b5Qd/Gy/R8xPznTyLAdcYVoO6Vs/73ExsGXD32xLqWf6bJfvjU88ylgTjJNk1tLeu3jdyKBGWyYslHVrLwW6LhAG9KKNUTxkc3fC33MvgaWzgRC/KaJEwoBdllHhxtL6llxdrxxp6S4y5iRd6RWxJHGALFr+RzQvg8dJNufexa67pxdo4xRQtvJBtzb5HrmtqtnE2PUuCscLaoKycI2NUfZ78/tfIb1PPebzr3q1xtCmil88hQiUMznjeO3PtRa2pTC2CCroRHAoEaD7xXLhrLLfJpmc/SD119INg1POZfuX5g0fj8YHuPqY6/dTzGT1jWI4bnhveKT319iNSP1hzwrNvU53pKVrXn9KJ/cGj83JS3zlULqjnPHLtJc8V9ZxHB0xKO9pyrTpA+oqurI91EjN5saYjaxF4WOPFmnPpxTxL9PzuffYDXf30fv/b0KBMoBfzbHkuNHMJA3oxT6kXR+pbenmxZawh+pbMwtTJHzlqbCG1JNYwRkYvrni8dHMuaVXLiy1xiqlrbeFF/9qlnrner/UT48HDTHouCcYKazyQhLB+FqU/84Pu3sa+h3rO4133bo2jjZGhfA4RImFwRncDt4HjA8sN0dm1Fudd0FW0Q9d/xfgyEzlHjLMio55vmH8Rmz6GZuFQz2de8ViWdkOnzxVlATPq+RfZpklf7/v93+YqXQmA39BV2taDuiuG9RTPlzQKretPoCsT+h7kuscafOo5j1xzSaeJeo7Tr0f7z/9cfdov2x+YXjKbyQudEGlx3hYv1pxLL8ZZo+dQ239F2RJyejHO1jpq6Drk3oegF+OsrWeO0Lds7YXFWEPOL32GRC8JCFkmDC5YHmuY+q7oXpzQ6S4BrhvKngnB2outcYoxWnkxVc+UaJNFTwmulgZjt5zXfyZlEgT1XH+eEKHu3RJHGyNL+ewTImFQg9IHweq8LSx5cL2gnrZQT1sy6SnZ6chQT1uopy2Z9NxCBi/esG720NrzvKAXcaAXcaAXcaAXcXhFndUelkT34owumD31fo8S6IUtGfR8wbog9drztkA9baGeddhtwiALsh9fpo5QZKinLdTTlhPWZ9vJX6inLdQzDvQiDvQiDvQiDvQiDvQiFp+o9z4Jsgx6YQv1tIV62kI968CEgSMvWPbCCTIN9bSFetoi+9ZtffEq6aCetlDPONCLONCLONCLONCLONCLWHxg+4uBiQ30whbqaQv1tIV61qNKbF/2VYu+NNKTE7pCXeOFSEeEetpCPe25Yv1LCMlfqKct1DMO9CIO9CIO9CIO9CIO9CIOF+Tb+nCv0AtbqKct1NMW6lmXT3SxfVON9RugOeOBEEIIIYQQQgghhBBCCImNLAT4QoUtyk/oVhjISoNXcLYyIYQQQgghhBBCCCGEEBKFF3ST/nUsv+r7TM/oMhNXcKkIIYQQQgghhBBCCCGEEBIFid2/oXKigBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghu+U/LRL9D6cX6ZgAAAAASUVORK5CYII=" style="width: 774px; height: 18.5px;" width="774" height="18.5"></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; 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: 380px 8px; transform-origin: 380px 8px; unicode-bidi: normal; "><span style="font-weight: 700; ">Create a program that calculates the total area of all non-squarable integer rectangles whose areas are less than or equal to a given area limit </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);">A</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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; "><span style="font-weight: 700; ">. </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: 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: 47.5px; height: 18px;" width="47.5" 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: 89.5px 8px; transform-origin: 89.5px 8px; unicode-bidi: normal; "><span style="">, the program should output:</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: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; "><span style="">        </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 668px; height: 18px;" width="668" height="18"></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: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; "><span style="font-weight: 700; ">NOTE:</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: 247.5px 8px; transform-origin: 247.5px 8px; unicode-bidi: normal; "><span style=""> Reflections and rotations are not significant and should be counted only once.</span></span></div></div></div>

Any integer-sided rectangle can be cut into unit rectangles () and rearranged into sets of smaller rectangles. For example the  rectangle can be broken as follows:
                                                      
We call an integer rectangle as "squarable" if it can be can be broken (i.e. cut into unit rectangles and rearranged) into any number of non-unit squares of equal sizes. For example the  rectangle can be broken into six  squares. Therefore, the  rectangle is squarable.
                                                
Integer rectangles that are not squarable are called "non-squarable". The  rectangle, shown in the first example above, is a non-squarable rectangle. The complete set of non-squarable rectangles with area  square units are as follows:

Create a program that calculates the total area of all non-squarable integer rectangles whose areas are less than or equal to a given area limit . 
For , the program should output:
        
NOTE: Reflections and rotations are not significant and should be counted only once.

Solve

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Problem 53109. Easy Sequences 52: Non-squarable Rectangles

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Problem 53109. Easy Sequences 52: Non-squarable Rectangles

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