EulerPhi[n] > n/(E^EulerGamma Log[Log[n]] + 2.50637/Log[Log[n]]) /; n >= 2

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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> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, EulerPhi] </annotation> </semantics> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mfrac> <mi> n </mi> <mrow> <mrow> <msup> <mi> &#8519; </mi> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[EulerGamma]] </annotation> </semantics> </msup> <mo> &#8290; </mo> <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> </mrow> <mo> + </mo> <mfrac> <mn> 2.50637 </mn> <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> </mrow> </mfrac> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8805; </mo> <mn> 2 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <gt /> <apply> <ci> EulerPhi </ci> <ci> n </ci> </apply> <apply> <times /> <ci> n </ci> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <eulergamma /> </apply> <apply> <ln /> <apply> <ln /> <ci> n </ci> </apply> </apply> </apply> <apply> <times /> <cn type='real'> 2.50637 </cn> <apply> <power /> <apply> <ln /> <apply> <ln /> <ci> n </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <geq /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

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2002-12-18