EulerPhi[n Floor[DivisorSigma[1, n]/n]] < 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> <mrow> <mi> n </mi> <mo> &#8290; </mo> <mrow> <mo> &#8970; </mo> <mfrac> <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> <mi> n </mi> </mfrac> <mo> &#8971; </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &lt; </mo> <mi> n </mi> </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> <lt /> <apply> <ci> EulerPhi </ci> <apply> <times /> <ci> n </ci> <apply> <floor /> <apply> <times /> <apply> <ci> DivisorSigma </ci> <cn type='integer'> 1 </cn> <ci> n </ci> </apply> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <ci> n </ci> </apply> <apply> <geq /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["EulerPhi", "[", RowBox[List["n", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["DivisorSigma", "[", RowBox[List["1", ",", "n"]], "]"]], "n"], "]"]]]], "]"]], "<", "n"]], "/;", RowBox[List["n", "\[GreaterEqual]", "2"]]]]]]

2002-12-18