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

Author

Jaroslav Krizek, Oct 18 2009

Keywords

• nonn
• mult

Links

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

Crossrefs

Cf. A001222, A165825.

Programs

Mathematica

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

PARI

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

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