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DivisorSigma




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/13.05.29.0004.01









  


  








Input Form





DivisorSigma[1, n] <= EulerPhi[n] + DivisorSigma[0, n] (n - EulerPhi[n])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["DivisorSigma", "[", RowBox[List["1", ",", "n"]], "]"]], "\[LessEqual]", RowBox[List[RowBox[List["EulerPhi", "[", "n", "]"]], "+", RowBox[List[RowBox[List["DivisorSigma", "[", RowBox[List["0", ",", "n"]], "]"]], " ", RowBox[List["(", RowBox[List["n", "-", RowBox[List["EulerPhi", "[", "n", "]"]]]], ")"]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <semantics> <mi> &#963; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Sigma]&quot;, DivisorSigma] </annotation> </semantics> <mn> 1 </mn> </msub> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> &#8804; </mo> <mrow> <mrow> <mrow> <msub> <semantics> <mi> &#963; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Sigma]&quot;, DivisorSigma] </annotation> </semantics> <mn> 0 </mn> </msub> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mrow> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, EulerPhi] </annotation> </semantics> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, EulerPhi] </annotation> </semantics> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <leq /> <apply> <ci> DivisorSigma </ci> <cn type='integer'> 1 </cn> <ci> n </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> DivisorSigma </ci> <cn type='integer'> 0 </cn> <ci> n </ci> </apply> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> EulerPhi </ci> <ci> n </ci> </apply> </apply> </apply> </apply> <apply> <ci> EulerPhi </ci> <ci> n </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["DivisorSigma", "[", RowBox[List["1", ",", "n"]], "]"]], "\[LessEqual]", RowBox[List[RowBox[List["EulerPhi", "[", "n", "]"]], "+", RowBox[List[RowBox[List["DivisorSigma", "[", RowBox[List["0", ",", "n"]], "]"]], " ", RowBox[List["(", RowBox[List["n", "-", RowBox[List["EulerPhi", "[", "n", "]"]]]], ")"]]]]]]]]]]


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





2002-12-18