A167328 Totally multiplicative sequence with a(p) = 9*(p+3) for prime p.

1, 45, 54, 2025, 72, 2430, 90, 91125, 2916, 3240, 126, 109350, 144, 4050, 3888, 4100625, 180, 131220, 198, 145800, 4860, 5670, 234, 4920750, 5184, 6480, 157464, 182250, 288, 174960, 306, 184528125, 6804, 8100, 6480, 5904900, 360, 8910, 7776, 6561000, 396, 218700

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (9*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (9*(p(k)+3))^e(k).

a(n) = A165830(n) * A166591(n) = 9^bigomega(n) * A166591(n) = 9^A001222(n) * A166591(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*9^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 09 2016 *)
f[p_, e_] := (9*(p+3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 21 2023 *)

Crossrefs

Cf. A001222, A165830, A166591.

Sequence in context: A085607 A087993 A062390 * A116247 A168108 A037042

Adjacent sequences: A167325 A167326 A167327 * A167329 A167330 A167331

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved