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DivisorSigma




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/13.05.29.0029.01









  


  








Input Form





DivisorSigma[0, m n]/DivisorSigma[0, m] >= DivisorSigma[1, m n]/ (n DivisorSigma[1, m])








Standard Form





Cell[BoxData[RowBox[List[FractionBox[RowBox[List["DivisorSigma", "[", RowBox[List["0", ",", RowBox[List["m", " ", "n"]]]], "]"]], RowBox[List["DivisorSigma", "[", RowBox[List["0", ",", "m"]], " ", "]"]]], "\[GreaterEqual]", FractionBox[RowBox[List["DivisorSigma", "[", RowBox[List["1", ",", RowBox[List["m", " ", "n"]]]], "]"]], RowBox[List["n", " ", RowBox[List["DivisorSigma", "[", RowBox[List["1", ",", " ", "m"]], "]"]]]]]]]]]








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> <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> </mrow> <mo> ) </mo> </mrow> <mrow> <msub> <semantics> <mi> &#963; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Sigma]&quot;, DivisorSigma] </annotation> </semantics> <mn> 0 </mn> </msub> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mfrac> <mo> &#8805; </mo> <mfrac> <mrow> <msub> <semantics> <mi> &#963; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Sigma]&quot;, DivisorSigma] </annotation> </semantics> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> &#963; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Sigma]&quot;, DivisorSigma] </annotation> </semantics> <mn> 1 </mn> </msub> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <geq /> <apply> <times /> <apply> <ci> DivisorSigma </ci> <cn type='integer'> 0 </cn> <apply> <times /> <ci> m </ci> <ci> n </ci> </apply> </apply> <apply> <power /> <apply> <ci> DivisorSigma </ci> <cn type='integer'> 0 </cn> <ci> m </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <ci> DivisorSigma </ci> <cn type='integer'> 1 </cn> <apply> <times /> <ci> m </ci> <ci> n </ci> </apply> </apply> <apply> <power /> <apply> <times /> <ci> n </ci> <apply> <ci> DivisorSigma </ci> <cn type='integer'> 1 </cn> <ci> m </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[FractionBox[RowBox[List["DivisorSigma", "[", RowBox[List["0", ",", RowBox[List["m", " ", "n"]]]], "]"]], RowBox[List["DivisorSigma", "[", RowBox[List["0", ",", "m"]], "]"]]], "\[GreaterEqual]", FractionBox[RowBox[List["DivisorSigma", "[", RowBox[List["1", ",", RowBox[List["m", " ", "n"]]]], "]"]], RowBox[List["n", " ", RowBox[List["DivisorSigma", "[", RowBox[List["1", ",", "m"]], "]"]]]]]]]]]


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





2002-12-18