Sum of divisor powers: Inequalities (formula 13.05.29.0021)

DivisorSigma

$Mathematica Notation$

Number Theory Functions

DivisorSigma[k,n]

Inequalities

http://functions.wolfram.com/13.05.29.0021.01

Input Form

DivisorSigma[1, n] > (EulerPhi[n] + n - 1)/DivisorSigma[0, n] /; n >= 2

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["DivisorSigma", "[", RowBox[List["1", ",", "n"]], "]"]], ">", FractionBox[RowBox[List[RowBox[List["EulerPhi", "[", "n", "]"]], "+", "n", "-", "1"]], RowBox[List["DivisorSigma", "[", RowBox[List["0", ",", "n"]], "]"]]]]], "/;", RowBox[List["n", "\[GreaterEqual]", "2"]]]]]]

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> σ </mi> <annotation encoding='Mathematica'> TagBox["\[Sigma]", DivisorSigma] </annotation> </semantics> <mn> 1 </mn> </msub> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> > </mo> <mfrac> <mrow> <mi> n </mi> <mo> + </mo> <mrow> <semantics> <mi> ϕ </mi> <annotation encoding='Mathematica'> TagBox["\[Phi]", EulerPhi] </annotation> </semantics> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <msub> <semantics> <mi> σ </mi> <annotation encoding='Mathematica'> TagBox["\[Sigma]", DivisorSigma] </annotation> </semantics> <mn> 0 </mn> </msub> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <gt /> <apply> <ci> DivisorSigma </ci> <cn type='integer'> 1 </cn> <ci> n </ci> </apply> <apply> <times /> <apply> <plus /> <ci> n </ci> <apply> <ci> EulerPhi </ci> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <ci> DivisorSigma </ci> <cn type='integer'> 0 </cn> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2002-12-18