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 EulerPhi

 http://functions.wolfram.com/13.06.23.0005.01

 Input Form

 Sum[EulerPhi[n]/n^s, {n, 1, Infinity}] == Zeta[s - 1]/Zeta[s] /; Re[s] > 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["n", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List["EulerPhi", "[", "n", "]"]], SuperscriptBox["n", "s"]]]], "\[Equal]", FractionBox[RowBox[List["Zeta", "[", RowBox[List["s", "-", "1"]], "]"]], RowBox[List["Zeta", "[", "s", "]"]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "s", "]"]], ">", "1"]]]]]]

 MathML Form

 n = 1 ϕ TagBox["\[Phi]", EulerPhi] ( n ) n s ζ ( s - 1 ) TagBox[RowBox[List["\[Zeta]", "(", TagBox[RowBox[List["s", "-", "1"]], Rule[Editable, True]], ")"]], InterpretTemplate[Function[\$CellContext`e, Zeta[\$CellContext`e]]]] ζ ( s ) TagBox[RowBox[List["\[Zeta]", "(", TagBox["s", Rule[Editable, True]], ")"]], InterpretTemplate[Function[\$CellContext`e, Zeta[\$CellContext`e]]]] /; Re ( s ) > 1 Condition n 1 EulerPhi n n s -1 Zeta s -1 Zeta s -1 s 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["n_", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List["EulerPhi", "[", "n_", "]"]], SuperscriptBox["n_", "s_"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["Zeta", "[", RowBox[List["s", "-", "1"]], "]"]], RowBox[List["Zeta", "[", "s", "]"]]], "/;", RowBox[List[RowBox[List["Re", "[", "s", "]"]], ">", "1"]]]]]]]]

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

 2001-10-29