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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
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
Sequence in context: A010152 A327155 A316786 * A276405 A066341 A181064
KEYWORD
easy,nonn,mult
AUTHOR
STATUS
approved

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