Total[Divisors[n]^k] == DivisorSigma[k, n]

Cell[BoxData[RowBox[List[RowBox[List["Total", "[", SuperscriptBox[RowBox[List["Divisors", "[", "n", "]"]], "k"], "]"]], "\[Equal]", RowBox[List["DivisorSigma", "[", RowBox[List["k", ",", "n"]], "]"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <munder> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> | </mo> <mi> n </mi> </mrow> </munder> <msup> <mi> k </mi> <mi> n </mi> </msup> </mrow> <mo> &#10869; </mo> <mrow> <msub> <semantics> <mi> &#963; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Sigma]&quot;, DivisorSigma] </annotation> </semantics> <mi> k </mi> </msub> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> FormBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> UnderscriptBox </ci> <apply> <ci> ErrorBox </ci> <ms> &#8721; </ms> </apply> <apply> <ci> RowBox </ci> <list> <ms> k </ms> <ms> | </ms> <ms> n </ms> </list> </apply> </apply> <apply> <ci> SuperscriptBox </ci> <ms> k </ms> <ms> n </ms> </apply> </list> </apply> <ms> &#10869; </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <apply> <ci> TagBox </ci> <ms> &#963; </ms> <ci> DivisorSigma </ci> </apply> <ms> k </ms> </apply> <ms> ( </ms> <ms> n </ms> <ms> ) </ms> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Total", "[", SuperscriptBox[RowBox[List["Divisors", "[", "n_", "]"]], "k"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["DivisorSigma", "[", RowBox[List["k", ",", "n"]], "]"]]]]]]

2007-05-02