A167310 Totally multiplicative sequence with a(p) = 9*(p+2) for prime p.

1, 36, 45, 1296, 63, 1620, 81, 46656, 2025, 2268, 117, 58320, 135, 2916, 2835, 1679616, 171, 72900, 189, 81648, 3645, 4212, 225, 2099520, 3969, 4860, 91125, 104976, 279, 102060, 297, 60466176, 5265, 6156, 5103, 2624400, 351, 6804, 6075, 2939328, 387, 131220, 405

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (9*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (9*(p(k)+2))^e(k).

a(n) = A165830(n) * A166590(n) = 9^bigomega(n) * A166590(n) = 9^A001222(n) * A166590(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 2)^fi[[All, 2]])); Table[a[n]*9^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 07 2016 *)
f[p_, e_] := (9*(p+2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 19 2023 *)

Crossrefs

Cf. A001222, A165830, A166590.

Sequence in context: A068143 A264961 A188630 * A083674 A160063 A260927

Adjacent sequences: A167307 A167308 A167309 * A167311 A167312 A167313

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved