DivisorSigma[k, n] >= EulerPhi[n]^k + DivisorSigma[0, n]^2 /; k >= 2 && n >= 3

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<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> <mi> k </mi> </msub> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> &#8805; </mo> <mrow> <msup> <mrow> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, EulerPhi] </annotation> </semantics> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> + </mo> <msup> <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> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> k </mi> <mo> &#8805; </mo> <mn> 2 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &#8805; </mo> <mn> 3 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <geq /> <apply> <ci> DivisorSigma </ci> <ci> k </ci> <ci> n </ci> </apply> <apply> <plus /> <apply> <power /> <apply> <ci> EulerPhi </ci> <ci> n </ci> </apply> <ci> k </ci> </apply> <apply> <power /> <apply> <ci> DivisorSigma </ci> <cn type='integer'> 0 </cn> <ci> n </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <and /> <apply> <geq /> <ci> k </ci> <cn type='integer'> 2 </cn> </apply> <apply> <geq /> <ci> n </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2002-12-18