Divisors[p^n] == Table[p^k, {k, 0, n}] /; Element[p, Primes] && Element[n, Integers] && n > 0

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> divisors </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mi> p </mi> <mi> n </mi> </msup> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> p </mi> <mo> , </mo> <msup> <mi> p </mi> <mn> 2 </mn> </msup> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msup> <mi> p </mi> <mi> n </mi> </msup> </mrow> <mo> } </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> p </mi> <mo> &#8712; </mo> <semantics> <mi> &#8473; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalP]&quot;, Function[Primes]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> divisors </ci> <apply> <power /> <ci> p </ci> <ci> n </ci> </apply> </apply> <list> <cn type='integer'> 1 </cn> <ci> p </ci> <apply> <power /> <ci> p </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; </ci> <apply> <power /> <ci> p </ci> <ci> n </ci> </apply> </list> </apply> <apply> <and /> <apply> <in /> <ci> p </ci> <primes /> </apply> <apply> <in /> <ci> n </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2001-10-29