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 DivisorSigma

 http://functions.wolfram.com/13.05.06.0005.01

 Input Form

 DivisorSigma[k, n] == Sum[m^(k - 1) Sum[Cos[(2 Pi j n)/m], {j, 1, m}], {m, 1, n}]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["DivisorSigma", "[", RowBox[List["k", ",", "n"]], "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", "1"]], "n"], RowBox[List[SuperscriptBox["m", RowBox[List["k", "-", "1"]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "1"]], "m"], RowBox[List["Cos", "[", FractionBox[RowBox[List["2", "\[Pi]", " ", "j", " ", "n"]], "m"], "]"]]]]]]]]]]]]

 MathML Form

 σ TagBox["\[Sigma]", DivisorSigma] k ( n ) m = 1 n m k - 1 j = 1 m cos ( 2 π j n m ) DivisorSigma k n m 1 n m k -1 j 1 m 2 j n m -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DivisorSigma", "[", RowBox[List["k", ",", "n_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", "1"]], "n"], RowBox[List[SuperscriptBox["m", RowBox[List["k", "-", "1"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "1"]], "m"], RowBox[List["Cos", "[", FractionBox[RowBox[List["2", " ", "\[Pi]", " ", "j", " ", "n"]], "m"], "]"]]]]]]]]]]]]

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

 2007-05-02