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A166625 Totally multiplicative sequence with a(p) = 4p for prime p. 1

%I

%S 1,8,12,64,20,96,28,512,144,160,44,768,52,224,240,4096,68,1152,76,

%T 1280,336,352,92,6144,400,416,1728,1792,116,1920,124,32768,528,544,

%U 560,9216,148,608,624,10240,164,2688,172,2816,2880,736,188,49152,784,3200

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

%H G. C. Greubel, <a href="/A166625/b166625.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%F Dirichlet g.f.: Product_{p prime} 1 / (1 - 4 * p^(1 - s)). - _Ilya Gutkovskiy_, Oct 30 2019

%t Table[n 4^PrimeOmega[n],{n,50}] (* _Harvey P. Dale_, Jan 20 2014 *)

%o (PARI) a(n) = n*4^bigomega(n); \\ _Altug Alkan_, May 19 2016

%Y Cf. A001222, A165825.

%K nonn,mult

%O 1,2

%A _Jaroslav Krizek_, Oct 18 2009

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Last modified January 20 14:02 EST 2020. Contains 331094 sequences. (Running on oeis4.)