A166625 Totally multiplicative sequence with a(p) = 4p for prime p.

1, 8, 12, 64, 20, 96, 28, 512, 144, 160, 44, 768, 52, 224, 240, 4096, 68, 1152, 76, 1280, 336, 352, 92, 6144, 400, 416, 1728, 1792, 116, 1920, 124, 32768, 528, 544, 560, 9216, 148, 608, 624, 10240, 164, 2688, 172, 2816, 2880, 736, 188, 49152, 784, 3200

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Formula

Multiplicative with a(p^e) = (4p)^e.

If n = Product p(k)^e(k) then a(n) = Product (4*p(k))^e(k).

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

Dirichlet g.f.: Product_{p prime} 1 / (1 - 4 * p^(1 - s)). - Ilya Gutkovskiy, Oct 30 2019

Mathematica

Table[n 4^PrimeOmega[n], {n, 50}] (* Harvey P. Dale, Jan 20 2014 *)

Prog

(PARI) a(n) = n*4^bigomega(n); \\ Altug Alkan, May 19 2016

Crossrefs

Cf. A001222, A165825.

Sequence in context: A368125 A305236 A069186 * A370651 A038290 A002288

Adjacent sequences: A166622 A166623 A166624 * A166626 A166627 A166628

Keyword

nonn,mult

Author

Jaroslav Krizek, Oct 18 2009

Status

approved