A167307 Totally multiplicative sequence with a(p) = 6*(p+2) for prime p.

1, 24, 30, 576, 42, 720, 54, 13824, 900, 1008, 78, 17280, 90, 1296, 1260, 331776, 114, 21600, 126, 24192, 1620, 1872, 150, 414720, 1764, 2160, 27000, 31104, 186, 30240, 198, 7962624, 2340, 2736, 2268, 518400, 234, 3024, 2700, 580608, 258, 38880, 270

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (6*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (6*(p(k)+2))^e(k).

a(n) = A165827(n) * A166590(n) = 6^bigomega(n) * A166590(n) = 6^A001222(n) * A166590(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 2)^fi[[All, 2]])); Table[a[n]*6^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 07 2016 *)
f[p_, e_] := (6*(p+2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 19 2023 *)

Crossrefs

Cf. A001222, A165827, A166590.

Sequence in context: A067952 A239801 A123200 * A161378 A206448 A266984

Adjacent sequences: A167304 A167305 A167306 * A167308 A167309 A167310

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved