Problem 58018. List the Fermi-Dirac primes

Created by ChrisR

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{"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 Fermi-Dirac “primes” are prime powers with exponents that are powers of 2. The first nine terms of the sequence are 2, 3, 4, 5, 7, 9, 11, 13, and 16. Six of the terms are primes; two are squares of primes; and the remaining term, 16, is </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"2^4\"/></w:customXmlPr><w:r><w:t>2^4</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>The name comes from an analogy with particle physics because every number can be written as the product of a unique subset of the Fermi-Dirac primes. For example, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"2250 = 2x5x9x25\"/></w:customXmlPr><w:r><w:t>2250 = 2 \\cdot5\\cdot9\\cdot25</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>Write a function analogous to </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>primes(n)</w:t></w:r><w:r><w:t> that lists the Fermi-Dirac primes less than or equal to </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"n\"/></w:customXmlPr><w:r><w:t>n</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: 123px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 61.5px; transform-origin: 407px 61.5px; 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: 383.892px 8px; transform-origin: 383.892px 8px; unicode-bidi: normal; "><span style="">The Fermi-Dirac “primes” are prime powers with exponents that are powers of 2. The first nine terms of the sequence are 2, 3, 4, 5, 7, 9, 11, 13, and 16. Six of the terms are primes; two are squares of primes; and the remaining term, 16, is </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAmCAYAAAA820BcAAAB9ElEQVRYR+2WsS4FQRSG730E9CJErRESoVEgJCoSiQfAlSg1WvEACqK7HUKiEzQKIiQKenRKhCfw/zJHjt2du3PWri3sJn9md3Z2vpn/nJnZeq3Eq14iu1bBi3R/Dp1/QMdRSNG2DwN4AW1Aa38NfwCwpwz4KqCzUP9v4LRuyFn2jvIauk9Jkj68P4ems9pOaNPZFmXto2IZevEM4gT1my7RzDGXRGHfpw4wgLJNwVg/nzCABdRx5g3InHAd+OgGYrKwgycF5LLZUoNYxP2Oet+N+zNozH1nhhOwDg16bOX7XQfk7CcUnHY3oT1XZ4ZLvGKbgoK8utm/oWx39ZMoVyKDMcMZs0PPrIXPAY5DGs46hkwnIZ+51B4hhvEI+g5T1h1O4Mx6hoEXy07lDm+7oCXoFjqArqBLaZMVLrZPoaNW4THbHhl87JHL6M7NhsnmW+v8MHc4lxqtHNEWekbMpTcTtTur7TLrxFMqzbLoe0vMmblMNGauJJmV96O9BU67aWPSlpppEKHw3MEcbQi8EHAInD8EoylWc1t9htLO+FhoWs1cTjBuj/pk053IT0NvynpPzAkfXE4u2ZN9CcX9fRvi0Wu+kuD6yAzpMGSzCZ454xx68Z9O/0yEfvfVLiTbTR1aGldwi1u5ta1sz81KS0f/1/ZP3RZqJ7Kpf4cAAAAASUVORK5CYII=" alt="2^4" style="width: 15.5px; height: 19px;" width="15.5" height="19"></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: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; "><span style="">. </span></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: 373.808px 8px; transform-origin: 373.808px 8px; unicode-bidi: normal; "><span style="">The name comes from an analogy with particle physics because every number can be written as the product of a unique subset of the Fermi-Dirac primes. For example, </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="2250 = 2x5x9x25" style="width: 122px; height: 18px;" width="122" 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: 1.94167px 8px; transform-origin: 1.94167px 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: 92.45px 8px; transform-origin: 92.45px 8px; unicode-bidi: normal; "><span style="">Write a function analogous to </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: 34.65px 8px; transform-origin: 34.65px 8px; unicode-bidi: normal; "><span style="font-family: Menlo, Monaco, Consolas, &quot;Courier New&quot;, monospace; ">primes(n)</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: 167.633px 8px; transform-origin: 167.633px 8px; unicode-bidi: normal; "><span style=""> that lists the Fermi-Dirac primes less than or equal 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: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; "><span style="">.</span></span></div></div></div>

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Problem 58018. List the Fermi-Dirac primes

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