A167325 Totally multiplicative sequence with a(p) = 6*(p+3) for prime p.

1, 30, 36, 900, 48, 1080, 60, 27000, 1296, 1440, 84, 32400, 96, 1800, 1728, 810000, 120, 38880, 132, 43200, 2160, 2520, 156, 972000, 2304, 2880, 46656, 54000, 192, 51840, 204, 24300000, 3024, 3600, 2880, 1166400, 240, 3960, 3456, 1296000, 264, 64800, 276, 75600

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (6*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (6*(p(k)+3))^e(k).

a(n) = A165827(n) * A166591(n) = 6^bigomega(n) * A166591(n) = 6^A001222(n) * A166591(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*6^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 09 2016 *)
f[p_, e_] := (6*(p+3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 21 2023 *)

Crossrefs

Cf. A001222, A165827, A166591.

Sequence in context: A345382 A227680 A109426 * A051657 A257439 A298366

Adjacent sequences: A167322 A167323 A167324 * A167326 A167327 A167328

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved