A167327 Totally multiplicative sequence with a(p) = 8*(p+3) for prime p.

1, 40, 48, 1600, 64, 1920, 80, 64000, 2304, 2560, 112, 76800, 128, 3200, 3072, 2560000, 160, 92160, 176, 102400, 3840, 4480, 208, 3072000, 4096, 5120, 110592, 128000, 256, 122880, 272, 102400000, 5376, 6400, 5120, 3686400, 320, 7040, 6144, 4096000, 352, 153600

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

Multiplicative with a(p^e) = (8*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (8*(p(k)+3))^e(k).

a(n) = A165829(n) * A166591(n) = 8^bigomega(n) * A166591(n) = 8^A001222(n) * A166591(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*8^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 09 2016 *)
f[p_, e_] := (8*(p+3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 21 2023 *)

Crossrefs

Cf. A001222, A165829, A166591.

Sequence in context: A120382 A290017 A062909 * A216305 A173337 A167311

Adjacent sequences: A167324 A167325 A167326 * A167328 A167329 A167330

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved