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DivisorSigma




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/13.05.29.0007.01









  


  








Input Form





DivisorSigma[0, n] <= 2^(1.5379 (Log[n]/Log[Log[n]])) /; n >= 3








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["DivisorSigma", "[", RowBox[List["0", ",", "n"]], "]"]], "\[LessEqual]", SuperscriptBox["2", RowBox[List["1.5379", " ", FractionBox[RowBox[List["Log", "[", "n", "]"]], RowBox[List["Log", "[", RowBox[List["Log", "[", "n", "]"]], "]"]]]]]]]], "/;", RowBox[List["n", "\[GreaterEqual]", "3"]]]]]]








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> &#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> &#8804; </mo> <msup> <mn> 2 </mn> <mfrac> <mrow> <mn> 1.5379 </mn> <mtext> </mtext> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mfrac> </msup> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8805; </mo> <mn> 3 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <leq /> <apply> <ci> DivisorSigma </ci> <cn type='integer'> 0 </cn> <ci> n </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='real'> 1.5379 </cn> <apply> <ln /> <ci> n </ci> </apply> <apply> <power /> <apply> <ln /> <apply> <ln /> <ci> n </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <geq /> <ci> n </ci> <cn type='integer'> 3 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["DivisorSigma", "[", RowBox[List["0", ",", "n"]], "]"]], "\[LessEqual]", SuperscriptBox["2", FractionBox[RowBox[List["1.5379`", " ", RowBox[List["Log", "[", "n", "]"]]]], RowBox[List["Log", "[", RowBox[List["Log", "[", "n", "]"]], "]"]]]]]], "/;", RowBox[List["n", "\[GreaterEqual]", "3"]]]]]]


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





2002-12-18