Sum of divisor powers: Inequalities (formula 13.05.29.0018)

DivisorSigma

$Mathematica Notation$

Number Theory Functions

DivisorSigma[k,n]

Inequalities

http://functions.wolfram.com/13.05.29.0018.01

Input Form

DivisorSigma[1, n] < E^EulerGamma n Log[Log[n]] /; n >= 5041

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["DivisorSigma", "[", RowBox[List["1", ",", "n"]], "]"]], "<", RowBox[List[SuperscriptBox["\[ExponentialE]", "EulerGamma"], " ", "n", " ", RowBox[List["Log", "[", RowBox[List["Log", "[", "n", "]"]], "]"]]]]]], "/;", RowBox[List["n", "\[GreaterEqual]", "5041"]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <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> <mrow> <msup> <mi> ⅇ </mi> <semantics> <mi> ℽ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubledGamma]", Function[EulerGamma]] </annotation> </semantics> </msup> <mo> ⁢ </mo> <mi> n </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> ≥ </mo> <mn> 5041 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <lt /> <apply> <ci> DivisorSigma </ci> <cn type='integer'> 1 </cn> <ci> n </ci> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <eulergamma /> </apply> <ci> n </ci> <apply> <ln /> <apply> <ln /> <ci> n </ci> </apply> </apply> </apply> </apply> <apply> <geq /> <ci> n </ci> <cn type='integer'> 5041 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2002-12-18