A011264 In the prime factorization of n, increment even powers and decrement odd powers (multiplicative).

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

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