A167323 Totally multiplicative sequence with a(p) = 4*(p+3) for prime p.

1, 20, 24, 400, 32, 480, 40, 8000, 576, 640, 56, 9600, 64, 800, 768, 160000, 80, 11520, 88, 12800, 960, 1120, 104, 192000, 1024, 1280, 13824, 16000, 128, 15360, 136, 3200000, 1344, 1600, 1280, 230400, 160, 1760, 1536, 256000, 176, 19200, 184, 22400

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (4*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (4*(p(k)+3))^e(k).

a(n) = A165825(n) * A166591(n) = 4^bigomega(n) * A166591(n) = 4^A001222(n) * A166591(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*4^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 09 2016 *)
f[p_, e_] := (4*(p+3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 22 2023 *)

Crossrefs

Cf. A001222, A165825, A166591.

Sequence in context: A107302 A219392 A193572 * A112819 A070684 A295152

Adjacent sequences: A167320 A167321 A167322 * A167324 A167325 A167326

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved