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DivisorSigma






Mathematica Notation

Traditional Notation









Number Theory Functions > DivisorSigma[k,n] > Identities > Functional identities





http://functions.wolfram.com/13.05.17.0005.01









  


  










Input Form





DivisorSum[Subscript[d, j]^\[Mu] DivisorSigma[\[Mu], Subscript[d, j]], {Subscript[d, j], n}] == DivisorSum[(n/Subscript[d, j])^(2 \[Mu]) DivisorSigma[\[Mu], Subscript[d, j]], {Subscript[d, j], n}] /; Element[Subscript[d, j], Divisors[n]] && Element[\[Mu], Integers]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DivisorSum", "[", RowBox[List[RowBox[List[SubsuperscriptBox["d_", "j", "\[Mu]_"], " ", RowBox[List["DivisorSigma", "[", RowBox[List["\[Mu]_", ",", SubscriptBox["d_", "j"]]], "]"]]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["d_", "j"], ",", "n_"]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["DivisorSum", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["n", SubscriptBox["d", "j"]], ")"]], RowBox[List["2", " ", "\[Mu]"]]], " ", RowBox[List["DivisorSigma", "[", RowBox[List["\[Mu]", ",", SubscriptBox["d", "j"]]], "]"]]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["d", "j"], ",", "n"]], "}"]]]], "]"]], "/;", RowBox[List[RowBox[List[SubscriptBox["d", "j"], "\[Element]", RowBox[List["Divisors", "[", "n", "]"]]]], "&&", RowBox[List["\[Mu]", "\[Element]", "Integers"]]]]]]]]]]










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





2001-10-29