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EulerPhi






Mathematica Notation

Traditional Notation









Number Theory Functions > EulerPhi[n] > Representations through equivalent functions > With related functions





http://functions.wolfram.com/13.06.27.0006.01









  


  










Input Form





EulerPhi[n] DivisorSum[ ((Subscript[d, j] KroneckerDelta[GCD[m, Subscript[d, j]], 1])/ EulerPhi[Subscript[d, j]]) MoebiusMu[n/Subscript[d, j]], {Subscript[d, j], n}] == MoebiusMu[n] DivisorSum[Subscript[d, j] MoebiusMu[n/Subscript[d, j]], {Subscript[d, j], GCD[m, n]}] /; Element[Subscript[d, j], Divisors[n]] && Element[n, Integers] && n > 0 && Element[m, Integers] && m > 0










Standard Form





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MathML Form







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</mo> <mo> ( </mo> <mrow> <mi> m </mi> <mo> , </mo> <msub> <mi> d </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> </msub> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#956; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Mu]&quot;, MoebiusMu] </annotation> </semantics> <mo> ( </mo> <mfrac> <mi> n </mi> <msub> <mi> d </mi> <mi> j </mi> </msub> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <semantics> <mi> &#956; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Mu]&quot;, MoebiusMu] </annotation> </semantics> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <munder> <mo> &#8721; </mo> <mrow> <msub> <mi> d </mi> <mi> j </mi> </msub> <mo> | </mo> <mrow> <mi> gcd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> m </mi> <mo> , </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </munder> <mrow> <msub> <mi> d </mi> <mi> j </mi> </msub> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#956; 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</ms> <ci> MoebiusMu </ci> </apply> <ms> ( </ms> <apply> <ci> FractionBox </ci> <ms> n </ms> <apply> <ci> SubscriptBox </ci> <ms> d </ms> <ms> j </ms> </apply> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> </list> </apply> </list> </apply> <ms> /; </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> d </ms> <ms> j </ms> </apply> <ms> &#8712; </ms> <apply> <ci> RowBox </ci> <list> <ms> divisors </ms> <ms> ( </ms> <ms> n </ms> <ms> ) </ms> </list> </apply> </list> </apply> <ms> &#8743; </ms> <apply> <ci> RowBox </ci> <list> <ms> n </ms> <ms> &#8712; </ms> <apply> <ci> SuperscriptBox </ci> <ms> &#8469; </ms> <ms> + </ms> </apply> </list> </apply> <ms> &#8743; </ms> <apply> <ci> RowBox </ci> <list> <ms> m </ms> <ms> &#8712; </ms> <apply> <ci> SuperscriptBox </ci> <ms> &#8469; </ms> <ms> + </ms> </apply> </list> </apply> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29





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