A167322 Totally multiplicative sequence with a(p) = 3*(p+3) for prime p.

1, 15, 18, 225, 24, 270, 30, 3375, 324, 360, 42, 4050, 48, 450, 432, 50625, 60, 4860, 66, 5400, 540, 630, 78, 60750, 576, 720, 5832, 6750, 96, 6480, 102, 759375, 756, 900, 720, 72900, 120, 990, 864, 81000, 132, 8100, 138, 9450, 7776, 1170, 150, 911250, 900

Offset

1,2

Links

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

Formula

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

a(n) = A165824(n) * A166591(n) = 3^bigomega(n) * A166591(n) = 3^A001222(n) * A166591(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*3^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 09 2016 *)
f[p_, e_] := (3*(p+3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 22 2023 *)

Crossrefs

Cf. A001222, A165824, A166591.

Sequence in context: A083823 A222682 A220787 * A217406 A181664 A348517

Adjacent sequences: A167319 A167320 A167321 * A167323 A167324 A167325

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved