Problem 56553. Easy Sequences 81: Fibonacci Radicals

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/Radical_of_an_integer\"><w:r><w:t>radical of a positive integer</w:t></w:r></w:hyperlink><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>x</w:t></w:r></w:customXml><w:r><w:t> is defined as the product of the distinct prime numbers dividing </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>. For example, the distinct prime factors 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>100</w:t></w:r></w:customXml><w:r><w:t> 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>[2\\ 5]</w:t></w:r></w:customXml><w:r><w:t>, therefore the radical 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>100</w:t></w:r></w:customXml><w:r><w:t> 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>10</w:t></w:r></w:customXml><w:r><w:t>. Similarly, the radicals 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>14</w:t></w:r></w:customXml><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>125</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>1344</w:t></w:r></w:customXml><w:r><w:t> are </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>14</w:t></w:r></w:customXml><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>5</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>42</w:t></w:r></w:customXml><w:r><w:t>, respectively. The number</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>is considered to be the radical of itself.</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 index </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>, if </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>F_n</w:t></w:r></w:customXml><w:r><w:t> is the n-th </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Fibonacci_number\"><w:r><w:t>Fibonacci number </w:t></w:r></w:hyperlink><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>F_1=F_2=1</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>F_n=F_{n-1}+F_{n-2}</w:t></w:r></w:customXml><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&gt;2</w:t></w:r></w:customXml><w:r><w:t>), </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>write a function </w:t></w:r><w:r><w:rPr><w:b/><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>R(n)</w:t></w:r><w:r><w:t>,</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t> that calculates the radical 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>F_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, if </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=12</w:t></w:r></w:customXml><w:r><w:t> then </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>F_{12}=144=2^4\\times3^2</w:t></w:r></w:customXml><w:r><w:t>, therefore </w:t></w:r><w:r><w:rPr><w:b/><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>R(12) = 2 * 3 = 6</w:t></w:r><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>And, 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=24</w:t></w:r></w:customXml><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>F_{24}=46368 = 2^5 \\times 3^2 \\times 7 \\times 23</w:t></w:r></w:customXml><w:r><w:t>, therefore </w:t></w:r><w:r><w:rPr><w:b/><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>R(24) = 2 * 3 * 7 * 23 = 966</w:t></w:r><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>Since output can be large, please present </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>R(n)</w:t></w:r><w:r><w:t> as a string (double quotes) array of digits.</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: 20.440001px; 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: none; white-space: normal; "><div style="block-size: 208px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 104px; transform-origin: 407px 104px; vertical-align: baseline; "><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: 0px 0px; transform-origin: 0px 0px; ">The <a target='_blank' href = "https://en.wikipedia.org/wiki/Radical_of_an_integer">radical of a positive integer</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; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> 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; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> is defined as the product of the distinct prime numbers dividing 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; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">. For example, the distinct prime factors of <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; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> is <img src="data:image/png;base64,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" width="35.5" height="19" style="width: 35.5px; 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; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">, therefore the radical of <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; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> is <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; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">. Similarly, the radicals of <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; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">, <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; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> and <img src="data:image/png;base64,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" width="33" height="18" style="width: 33px; 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; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> are <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; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">, 5<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: 0px 0px; transform-origin: 0px 0px; "> and <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAJKADAAQAAAABAAAAJAAAAAAqDuP8AAACYElEQVRYCe2Wy0tVURSHLVOypAIHNTCwGgRBQVROBLkRBUHaqKBBYDnr+Sc4cVAOEqcFIkGDQiyRBk2DJg5MpEGJFEQPsoEgRC+0vh+cfVh3s/fxeO4dRJwFH3vt9TrbtR/ehoZSyg78Zx1oLPD39JNzExZgMSN/H74zcBF6oQ2+wRLUTY5R6Tf8gVORqk3YB+AXKM5nDFuRRpBWLVuZzoP7QGxB90yMi/XHx8Q0Q01yl2xbOLSgk0nMK8YTsBm2g2LnwOZrOwvLWTJV7HUySg8t6Bn2D7ATfGnBoHPnFjXsB+Sd7yLwK+hjV8EV9BfUiu8nXICY6IC7/JlQ0MaQ0bONMlfcJVCxmOzF8RwexQKwvzS+VaOn6qZUCyvXMJ+Gc/ApHJJadUZ0hrLkh3G+NXqqZnXoAFFDcB/G04zalA6T/sToqRpbUDMRD0AP3/U0unalJynxhXEiVC62ZYMEH4IKLEM9ZAtF3IG/gW63L7P+cbwrcCsQdQWbuyX+LQuEV5luJ7kPq6xrTHbgfw+6Ddo2X4ou6CiF9C9nGlr8onbub9kIzt2gR0ud8uWwMRxB35DMdcM+G59V25lMgv7QXvgOuWWWSLcl6xn14IVkG0Z1+yPsCQX4Nr9DeqyCD1aSqI64rsjkYkMPprZmCtTxbngHdZe8Z6iJLz8F3VD9ZIlJH47OmDOPPc+C9LbpJumsVCAm6pqu/n4b4G+Z9RXRtZ36mXIedMj7EhhS0YIPgt65F/AGCstaHbpD5XpchtwLvGw+qJZb6WKynsUsEZ/5JtnipV52oOxA2YGyA/9KB/4C2OmkMcnAvEAAAAAASUVORK5CYII=" 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; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">, respectively. The number1<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: 0px 0px; transform-origin: 0px 0px; ">is considered to be the radical of itself.</div><div style="block-size: 44px; 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 22px; text-align: left; transform-origin: 384px 22px; 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: 0px 0px; transform-origin: 0px 0px; ">For a given index 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; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">, if <img src="data:image/png;base64,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" width="17" height="20" style="width: 17px; height: 20px;"><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: 0px 0px; transform-origin: 0px 0px; "> is the n-th <a target='_blank' href = "https://en.wikipedia.org/wiki/Fibonacci_number">Fibonacci number </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; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">(<img src="data:image/png;base64,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" width="76" height="20" style="width: 76px; height: 20px;"><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: 0px 0px; transform-origin: 0px 0px; "> and <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANYAAAAoCAYAAACCewRHAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAA1qADAAQAAAABAAAAKAAAAADl+puhAAAHMElEQVR4Ae2bW4hVVRjH1YwxxbKMJqOaeai0C2Zlo2XaMFFalpQUaglSFBJYRBfoQbq+9CBUEplE2YNllJlCaqbWlJGiJlKZmYE6ZVoaXSzUzOr3H/fCNdt99uXMPufM3nt98J/1rW/d/3ut9a299plu3Zw4BhwDjgHHgGPAMeAYcAw4BhwDjgHHgGPAMeAYcAw4BhwDxWKge8Rw55I+FkTlC6rmEYwvByVkzHYp/V0K6sro917KnFNGuSIVySW/PSOe4GTSTwYLwSgr7yr0JeB3oDr6gvPACGAm0i70PMgGBnE6GAfEg5GDKDNBG/gX9AKnAU2UkV78O0In4QwUmt8X4OY/D/sItZCCRItsMVDe+qAMGbad6o3L8PBkyFi0wWixzQrJ45I6MlBIflvhwEyoRR35OCZ2D5Ydx1izb2hmCIYDhZdEDGkn6XdG5MlS8rt09hMwvkKdbqbe3PDbIwZJvckz3Mr3vqUHqdqp1wUlZNx2jdX/3egbrXiQmjceNAd0xD0jaLAp2ArH7w2QZu8kjTFIPC5GnqxlWUuHDQ+vxeh83jjQO7PGPy3G2MvJkit+43is0RZLW9C3W3GperHX7ddJinhy2Cg5CXX+v8waS5DXnkH6M1aevHFgDS11tZD8ajGZnfo5H6VamPOAdps8yyQGZzjQgunvG+wQ4rollHfPq1TSY+WO36jr9kZmia7RjfyE0gR0K3g+uAW0gEdBpWQYFetqv7PyORVcV2YlttfeQx0NYBCQtx4KdDzaD1YAJ8kZKBy/U+HI7NRhofl2lZzS6BK6ug5rO27amuimSub4MUYf5pYsnY+ESnqs3PEb5bHsnWQV8+Mh0AvoTHwxmA6+BpX8ELqJ+rXAOyttZVYwmHIDrLKT0beB3uAsoL7Jqy4ATpIzUDh+tej0ywrjEbSo/LIZw+N+Y87i+mmW4eBXdP9t3wRsf4ETQJZFG8MvIdDnA/GgsYblu4r0JJJLfsM81hWwc6LF0DJLN6p+wvOOieQ0HGONayW6/7ZPHCwF+618tVSPp/G7gE4WzyfoSF/ynhIjvzy1UErUfhLJCr+6qBOvo4B4Wg9eB1vBMRK2sOxjoM7AX/lKqyFdMfvtvmyZjvah9/YO/EHAaL7EtiHAXm2TnuUUMB00gtkgiTxB5rdDCpj65pNneUi+LSFp/qSs8KtTijbPa60BjEXXpZU2Bi2y2LKOnOYINCd2qfQzDqPKsKNH3LSgRRHVW5FnOFDYEFWghun6idUEMAuory+BNGUXlaleTaa0JCv83s+AvwE3A51QpgA5FPGhU0xs0eWEjjwqKEwEtZJa3grOZNCGAxGbBbmDTqrPWVhYWeF3LXxe5Hv4gzyeDxDW+dLa/+XDb1Nc33t01JPoIa1o18r7051icqX/eMXViYOeHifYRKapcTJG5GmLSA9Kts//5Xg8u069exzyDOJWnJi4Zy5ckAV+NX9fBf5XHm20fwLN69jPUe7N7NSa2ElFHu9Z0Ap+AyLwQrAG6HZpHujqMpIOGg4U3lZGh1VGY9VD+AxoMT0GxMkfYChIW7LisbLKr3le+jGy5sVCY7BD45Vs2zgiLZZBNyD1VjyOqmv6N8FwoMn0M5gP3gM6YtovgUS7nOg29ClfrwYS1+6VRFaTWQtIZReDF8Fg8CnQLZz4KaLkgV9tDJK5R4KOf/0L61uSF3XM0v6zHd0KJvFcco27QB2Ql5oD9OKn61+1uRl0VZlIx/aCZl8HnyYuTzPJZw+L/kCijoCShiNBt1sJzfhN6CUVIsgLv/fytF4BchhVlbtpTa5SZ9DxXsujPZvfG3jJuQy+98b8MaE2GslqcADYH5V1Q7YvAXqRN0gqdRTcSWN6ntOCGq2hLS6/6qJOCnE5Dpuj91GPPrPYz4/oUel5VE1d0wWIZDlY0K4dPQIu8+J5Dy5ggGd6g5xKqEubfuBy8BHYD4zsRnnDRCJCvafqVFBNaaGx/mBbNRuNaCsJv6pqBYh78lpfou0x2B8EzcB+fkQrLz1oQt+XNJEarOa+QNdxqpIL2mqu5uoD9EC7/GyrJ/Lesj1s2dJUK+Wx0uxjWnVVm98r6bg2loG+AZQ6PfiydT7aRBWaPMZTqcZ6y6aPbDfKmHNZwvjEgy4sjOgCw9huR0/7oRRpYVWT3yE8q+1AH+Jt0T/4rgMdjoXyLJUQcwy0X+y02iU7wFtAZ+M8Sx2DuxpsBfLURkag6P1Kx8HrPZ0gNWnyajo7tRq7ZkXV5FceSq8vWjzmM1Irut7Z2sBGUJVj4UoaOgT6ASOaZNqp94CbjDHHoa5jNd4ZvjF+SFzvSAtBh13Oly9p9FwKiPe/gdo9DOaBFpBHqRa/cj5yBuK0FMxmVjOeG2m5KO9XpUjuQ8KAUonO3mkGHL+dptBV4BhwDDgGHAOOAceAY8Ax4BhwDDgGHAOOAceAY8Ax4BhwDDgGHAOOgS7BwP+i3xvGKSehXQAAAABJRU5ErkJggg==" width="107" height="20" style="width: 107px; height: 20px;"><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: 0px 0px; transform-origin: 0px 0px; "> for <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; perspective-origin: 0px 0px; transform-origin: 0px 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; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">write a function <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: 0px 0px; transform-origin: 0px 0px; ">R(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; perspective-origin: 0px 0px; transform-origin: 0px 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; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> that calculates the radical of <img src="data:image/png;base64,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" width="17" height="20" style="width: 17px; height: 20px;"><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: 0px 0px; transform-origin: 0px 0px; ">.</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: 0px 0px; transform-origin: 0px 0px; ">For example, if <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; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> then <img src="data:image/png;base64,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" width="123" height="21" style="width: 123px; height: 21px;"><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: 0px 0px; transform-origin: 0px 0px; ">, therefore <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: 0px 0px; transform-origin: 0px 0px; ">R(12) = 2 * 3 = 6<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: 0px 0px; transform-origin: 0px 0px; ">. </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: 0px 0px; transform-origin: 0px 0px; ">And, 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; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">, <img 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" width="193" height="21" style="width: 193px; height: 21px;"><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: 0px 0px; transform-origin: 0px 0px; ">, therefore <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: 0px 0px; transform-origin: 0px 0px; ">R(24) = 2 * 3 * 7 * 23 = 966<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: 0px 0px; transform-origin: 0px 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; 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: 0px 0px; transform-origin: 0px 0px; ">Since output can be large, please present <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: 0px 0px; transform-origin: 0px 0px; ">R(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; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> as a string (double quotes) array of digits.</div></div></div>

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Last Solution submitted on Dec 27, 2022

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GeeTwo on 23 Dec 2022

The "hidden rules" on this one are quite a bit different!
Forbidden strings are: persistent global regex [ {
So java and BigInteger are allowed, but not literal arrays or cell arrays?
The largest number to radicalize is fib(10000).

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Solution 10192872

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1 Comment

GeeTwo on 24 Dec 2022

My first working solution was around 150, but as I prodded and poked, it got a lot shorter.

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Problem 56553. Easy Sequences 81: Fibonacci Radicals

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Problem 56553. Easy Sequences 81: Fibonacci Radicals

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