A167304 Totally multiplicative sequence with a(p) = 3*(p+2) for prime p.

1, 12, 15, 144, 21, 180, 27, 1728, 225, 252, 39, 2160, 45, 324, 315, 20736, 57, 2700, 63, 3024, 405, 468, 75, 25920, 441, 540, 3375, 3888, 93, 3780, 99, 248832, 585, 684, 567, 32400, 117, 756, 675, 36288, 129, 4860, 135, 5616, 4725, 900, 147, 311040, 729, 5292

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (3*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (3*(p(k)+2))^e(k).

a(n) = A165824(n) * A166590(n) = 3^bigomega(n) * A166590(n) = 3^A001222(n) * A166590(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 2)^fi[[All, 2]])); Table[a[n]*3^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 07 2016 *)
f[p_, e_] := (3*(p+2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 21 2023 *)

Crossrefs

Cf. A001222, A165824, A166590.

Sequence in context: A152190 A330367 A079322 * A191966 A333720 A135451

Adjacent sequences: A167301 A167302 A167303 * A167305 A167306 A167307

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved