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A166625 Totally multiplicative sequence with a(p) = 4p for prime p. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A298901 A305236 A069186 * A038290 A002288 A216711

Adjacent sequences:  A166622 A166623 A166624 * A166626 A166627 A166628

KEYWORD

nonn,mult

AUTHOR

Jaroslav Krizek, Oct 18 2009

STATUS

approved

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Last modified August 9 12:53 EDT 2022. Contains 356026 sequences. (Running on oeis4.)