%I #11 Oct 22 2023 00:51:32
%S 1,10,12,100,16,120,20,1000,144,160,28,1200,32,200,192,10000,40,1440,
%T 44,1600,240,280,52,12000,256,320,1728,2000,64,1920,68,100000,336,400,
%U 320,14400,80,440,384,16000,88,2400,92,2800,2304,520,100,120000,400,2560
%N Totally multiplicative sequence with a(p) = 2*(p+3) for prime p.
%H G. C. Greubel, <a href="/A167321/b167321.txt">Table of n, a(n) for n = 1..1000</a>
%F Multiplicative with a(p^e) = (2*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(p(k)+3))^e(k).
%F a(n) = A061142(n) * A166591(n) = 2^bigomega(n) * A166591(n) = 2^A001222(n) * A166591(n).
%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*2^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 09 2016 *)
%t f[p_, e_] := (2*(p+3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 22 2023 *)
%Y Cf. A001222, A061142, A166591.
%K nonn,easy,mult
%O 1,2
%A _Jaroslav Krizek_, Nov 01 2009
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