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DivisorSigma




Mathematica Notation

Traditional Notation









Number Theory Functions > DivisorSigma[k,n] > Inequalities





http://functions.wolfram.com/13.05.29.0028.01









  


  








Input Form





(DivisorSigma[0, m^2 n] DivisorSigma[0, k^2 n])/DivisorSigma[0, m n k]^2 >= (DivisorSigma[0, m^2] DivisorSigma[0, k^2])/DivisorSigma[0, m k]^2








Standard Form





Cell[BoxData[RowBox[List[FractionBox[RowBox[List[RowBox[List["DivisorSigma", "[", RowBox[List["0", ",", RowBox[List[SuperscriptBox[RowBox[List["m", " "]], "2"], "n"]]]], "]"]], RowBox[List["DivisorSigma", "[", RowBox[List["0", ",", RowBox[List[SuperscriptBox[RowBox[List["k", " "]], "2"], "n"]]]], "]"]]]], SuperscriptBox[RowBox[List["DivisorSigma", "[", RowBox[List["0", ",", " ", RowBox[List["m", " ", "n", " ", "k"]]]], "]"]], "2"]], "\[GreaterEqual]", FractionBox[RowBox[List[RowBox[List["DivisorSigma", "[", RowBox[List["0", ",", SuperscriptBox[RowBox[List["m", " "]], "2"]]], "]"]], RowBox[List["DivisorSigma", "[", RowBox[List["0", ",", SuperscriptBox[RowBox[List["k", " "]], "2"]]], "]"]]]], SuperscriptBox[RowBox[List["DivisorSigma", "[", RowBox[List["0", ",", RowBox[List["m", " ", "k"]]]], "]"]], "2"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <mrow> <msub> <semantics> <mi> &#963; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Sigma]&quot;, DivisorSigma] </annotation> </semantics> <mn> 0 </mn> </msub> <mo> ( </mo> <mrow> <msup> <mi> m </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> &#963; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Sigma]&quot;, DivisorSigma] </annotation> </semantics> <mn> 0 </mn> </msub> <mo> ( </mo> <mrow> <msup> <mi> k </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <msup> <mrow> <msub> <semantics> <mi> &#963; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Sigma]&quot;, DivisorSigma] </annotation> </semantics> <mn> 0 </mn> </msub> <mo> ( </mo> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> n </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> <mo> &#8805; </mo> <mfrac> <mrow> <mrow> <msub> <semantics> <mi> &#963; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Sigma]&quot;, DivisorSigma] </annotation> </semantics> <mn> 0 </mn> </msub> <mo> ( </mo> <msup> <mi> m </mi> <mn> 2 </mn> </msup> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> &#963; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Sigma]&quot;, DivisorSigma] </annotation> </semantics> <mn> 0 </mn> </msub> <mo> ( </mo> <msup> <mi> k </mi> <mn> 2 </mn> </msup> <mo> ) </mo> </mrow> </mrow> <msup> <mrow> <msub> <semantics> <mi> &#963; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Sigma]&quot;, DivisorSigma] </annotation> </semantics> <mn> 0 </mn> </msub> <mo> ( </mo> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <geq /> <apply> <times /> <apply> <ci> DivisorSigma </ci> <cn type='integer'> 0 </cn> <apply> <times /> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> <ci> n </ci> </apply> </apply> <apply> <ci> DivisorSigma </ci> <cn type='integer'> 0 </cn> <apply> <times /> <apply> <power /> <ci> k </ci> <cn type='integer'> 2 </cn> </apply> <ci> n </ci> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <ci> DivisorSigma </ci> <cn type='integer'> 0 </cn> <apply> <times /> <ci> m </ci> <ci> n </ci> <ci> k </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <ci> DivisorSigma </ci> <cn type='integer'> 0 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> DivisorSigma </ci> <cn type='integer'> 0 </cn> <apply> <power /> <ci> k </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <ci> DivisorSigma </ci> <cn type='integer'> 0 </cn> <apply> <times /> <ci> m </ci> <ci> k </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[FractionBox[RowBox[List[RowBox[List["DivisorSigma", "[", RowBox[List["0", ",", RowBox[List[SuperscriptBox["m", "2"], " ", "n"]]]], "]"]], " ", RowBox[List["DivisorSigma", "[", RowBox[List["0", ",", RowBox[List[SuperscriptBox["k", "2"], " ", "n"]]]], "]"]]]], SuperscriptBox[RowBox[List["DivisorSigma", "[", RowBox[List["0", ",", RowBox[List["m", " ", "n", " ", "k"]]]], "]"]], "2"]], "\[GreaterEqual]", FractionBox[RowBox[List[RowBox[List["DivisorSigma", "[", RowBox[List["0", ",", SuperscriptBox["m", "2"]]], "]"]], " ", RowBox[List["DivisorSigma", "[", RowBox[List["0", ",", SuperscriptBox["k", "2"]]], "]"]]]], SuperscriptBox[RowBox[List["DivisorSigma", "[", RowBox[List["0", ",", RowBox[List["m", " ", "k"]]]], "]"]], "2"]]]]]]


Date Added to functions.wolfram.com (modification date)





2002-12-18