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 GCD

 http://functions.wolfram.com/04.08.23.0003.01

 Input Form

 Sum[KroneckerDelta[1, GCD[k, n]]/(n^2 (k + n)), {n, 1, Infinity}, {k, 1, n}] == 3/4

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["n", "=", "1"]], "\[Infinity]"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "n"], FractionBox[RowBox[List["KroneckerDelta", "[", RowBox[List["1", ",", " ", RowBox[List["GCD", "[", RowBox[List["k", ",", "n"]], "]"]]]], "]"]], RowBox[List[SuperscriptBox["n", "2"], RowBox[List["(", RowBox[List["k", "+", "n"]], ")"]]]]]]]]], "\[Equal]", FractionBox["3", "4"]]]]]

 MathML Form

 n = 1 k = 1 n δ KroneckerDelta 1 , gcd ( k , n ) n 2 ( k + n ) 3 4 k 1 n n 1 KroneckerDelta 1 k n n 2 k n -1 3 4 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["n_", "=", "1"]], "\[Infinity]"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "1"]], "n_"], FractionBox[RowBox[List["KroneckerDelta", "[", RowBox[List["1", ",", RowBox[List["GCD", "[", RowBox[List["k_", ",", "n_"]], "]"]]]], "]"]], RowBox[List[SuperscriptBox["n_", "2"], " ", RowBox[List["(", RowBox[List["k_", "+", "n_"]], ")"]]]]]]]]], "]"]], "\[RuleDelayed]", FractionBox["3", "4"]]]]]

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

 2001-10-29