CarmichaelLambda[2^n] == (1/2) EulerPhi[2^n] /; 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> <semantics> <mi> &#955; </mi> <annotation-xml encoding='MathML-Content'> <ci> CarmichaelLambda </ci> </annotation-xml> </semantics> <mo> ( </mo> <msup> <mn> 2 </mn> <mi> n </mi> </msup> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, EulerPhi] </annotation> </semantics> <mo> ( </mo> <msup> <mn> 2 </mn> <mi> n </mi> </msup> <mo> ) </mo> </mrow> </mrow> </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> <eq /> <apply> <ci> CarmichaelLambda </ci> <apply> <power /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <ci> EulerPhi </ci> <apply> <power /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> </apply> </apply> </apply> <apply> <geq /> <ci> n </ci> <cn type='integer'> 3 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["CarmichaelLambda", "[", SuperscriptBox["2", "n_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["EulerPhi", "[", SuperscriptBox["2", "n"], "]"]], "2"], "/;", RowBox[List["n", "\[GreaterEqual]", "3"]]]]]]]]

2001-10-29