Problem 58019. Factor a number into Fermi-Dirac primes

Created by ChrisR

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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: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; 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; "><a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/58018"><span style=""><span style="">Cody Problem 58018</span></span></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: 318.25px 8px; transform-origin: 318.25px 8px; unicode-bidi: normal; "><span style=""> asked you to list the Fermi-Dirac primes, which are prime powers with exponents that are powers of 2. As noted there, 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: 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: 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; ">factor(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: 75.8333px 8px; transform-origin: 75.8333px 8px; unicode-bidi: normal; "><span style=""> that factors the number </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: 171.917px 8px; transform-origin: 171.917px 8px; unicode-bidi: normal; "><span style=""> into Fermi-Dirac primes. List the Fermi-Dirac primes in ascending order. Take the factorization of 1 to be 1. </span></span></div></div></div>

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Last Solution submitted on May 17, 2023

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Problem 58019. Factor a number into Fermi-Dirac primes

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Problem 58019. Factor a number into Fermi-Dirac primes

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