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 EulerPhi

 http://functions.wolfram.com/13.06.23.0001.01

 Input Form

 Sum[EulerPhi[k], {l, 1, n}, {k, 1, Floor[n/l]}] == (1/2) n (n + 1)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["l", "=", "1"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], RowBox[List["Floor", "[", FractionBox["n", "l"], "]"]]], RowBox[List["EulerPhi", "[", "k", "]"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", "n", " ", RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]]]]]]]]

 MathML Form

 l = 1 n k = 1 n l ϕ TagBox["\[Phi]", EulerPhi] ( k ) n ( n + 1 ) 2 k 1 n l -1 l 1 n EulerPhi k n n 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["l_", "=", "1"]], "n_"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], RowBox[List["Floor", "[", FractionBox["n_", "l_"], "]"]]], RowBox[List["EulerPhi", "[", "k", "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", "n", " ", RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]]]]]]]]

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

 2001-10-29