DivisorSigma[1, n] < 2.59 n Log[Log[n]] /; n >= 7

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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> <mn> 1 </mn> </msub> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> &lt; </mo> <mrow> <mn> 2.59 </mn> <mtext> </mtext> <mi> n </mi> <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> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8805; </mo> <mn> 7 </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 /> <cn type='real'> 2.59 </cn> <ci> n </ci> <apply> <ln /> <apply> <ln /> <ci> n </ci> </apply> </apply> </apply> </apply> <apply> <geq /> <ci> n </ci> <cn type='integer'> 7 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

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2002-12-18