DivisorSigma[k, m n] == DivisorSum[Subscript[d, j]^k MoebiusMu[Subscript[d, j]] DivisorSigma[k, m/Subscript[d, j]] DivisorSigma[k, n/Subscript[d, j]], {Subscript[d, j], GCD[n, m]}] /; Element[Subscript[d, j], Divisors[GCD[n, m]]]

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2001-10-29