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 A011264 In the prime factorization of n, increment even powers and decrement odd powers (multiplicative). 4
 1, 1, 1, 8, 1, 1, 1, 4, 27, 1, 1, 8, 1, 1, 1, 32, 1, 27, 1, 8, 1, 1, 1, 4, 125, 1, 9, 8, 1, 1, 1, 16, 1, 1, 1, 216, 1, 1, 1, 4, 1, 1, 1, 8, 27, 1, 1, 32, 343, 125, 1, 8, 1, 9, 1, 4, 1, 1, 1, 8, 1, 1, 27, 128, 1, 1, 1, 8, 1, 1, 1, 108, 1, 1, 125, 8, 1, 1, 1, 32, 243, 1, 1, 8, 1, 1, 1, 4, 1, 27, 1, 8, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA a(n) = Product_{k=1..A001221(n)} (A027748(n,k)^A004442(A124010(n,k))). - Reinhard Zumkeller, Jun 23 2013 From Amiram Eldar, Jan 07 2023: (Start) a(n) = n^2/A011262(n). a(n) = n*A007947(n)/A007913(n)^2. a(n) = n*A336643(n)/A007913(n). a(n) = A356191(n)/A007913(n). (End) Dirichlet g.f.: zeta(2*s-2) * Product_{p prime} (1 + 1/p^s + 1/p^(2*s-3) - 1/p^(2*s-2)). - Amiram Eldar, Sep 21 2023 MATHEMATICA f[n_, k_] := n^(If[EvenQ[k], k + 1, k - 1]); Table[Times @@ f @@@ FactorInteger[n], {n, 94}] (* Jayanta Basu, Aug 14 2013 *) PROG (Haskell) a011264 n = product \$ zipWith (^) (a027748_row n) (map a004442 \$ a124010_row n) -- Reinhard Zumkeller, Jun 23 2013 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^if(f[i, 2]%2, f[i, 2]-1, f[i, 2]+1)); } \\ Amiram Eldar, Jan 07 2023 CROSSREFS Cf. A001221, A004442, A007913, A007947, A011262, A027748, A336643, A356191. Sequence in context: A010152 A327155 A316786 * A276405 A066341 A181064 Adjacent sequences: A011261 A011262 A011263 * A011265 A011266 A011267 KEYWORD easy,nonn,mult AUTHOR Marc LeBrun STATUS approved

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Last modified June 18 00:47 EDT 2024. Contains 373468 sequences. (Running on oeis4.)