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%I #11 Oct 22 2023 00:51:04
%S 1,20,24,400,32,480,40,8000,576,640,56,9600,64,800,768,160000,80,
%T 11520,88,12800,960,1120,104,192000,1024,1280,13824,16000,128,15360,
%U 136,3200000,1344,1600,1280,230400,160,1760,1536,256000,176,19200,184,22400
%N Totally multiplicative sequence with a(p) = 4*(p+3) for prime p.
%H G. C. Greubel, <a href="/A167323/b167323.txt">Table of n, a(n) for n = 1..1000</a>
%F 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).
%F a(n) = A165825(n) * A166591(n) = 4^bigomega(n) * A166591(n) = 4^A001222(n) * A166591(n).
%t 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 *)
%t f[p_, e_] := (4*(p+3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 22 2023 *)
%Y Cf. A001222, A165825, A166591.
%K nonn,easy,mult
%O 1,2
%A _Jaroslav Krizek_, Nov 01 2009
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