A167321 Totally multiplicative sequence with a(p) = 2*(p+3) for prime p.

1, 10, 12, 100, 16, 120, 20, 1000, 144, 160, 28, 1200, 32, 200, 192, 10000, 40, 1440, 44, 1600, 240, 280, 52, 12000, 256, 320, 1728, 2000, 64, 1920, 68, 100000, 336, 400, 320, 14400, 80, 440, 384, 16000, 88, 2400, 92, 2800, 2304, 520, 100, 120000, 400, 2560

Offset

1,2

Links

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

Formula

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

a(n) = A061142(n) * A166591(n) = 2^bigomega(n) * A166591(n) = 2^A001222(n) * A166591(n).

Mathematica

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

Crossrefs

Cf. A001222, A061142, A166591.

Sequence in context: A241252 A336892 A301905 * A258484 A116118 A038314

Adjacent sequences: A167318 A167319 A167320 * A167322 A167323 A167324

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved