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%I #12 Oct 21 2023 05:33:34
%S 1,40,48,1600,64,1920,80,64000,2304,2560,112,76800,128,3200,3072,
%T 2560000,160,92160,176,102400,3840,4480,208,3072000,4096,5120,110592,
%U 128000,256,122880,272,102400000,5376,6400,5120,3686400,320,7040,6144,4096000,352,153600
%N Totally multiplicative sequence with a(p) = 8*(p+3) for prime p.
%H G. C. Greubel, <a href="/A167327/b167327.txt">Table of n, a(n) for n = 1..1000</a>
%F Multiplicative with a(p^e) = (8*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (8*(p(k)+3))^e(k).
%F a(n) = A165829(n) * A166591(n) = 8^bigomega(n) * A166591(n) = 8^A001222(n) * A166591(n).
%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*8^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 09 2016 *)
%t f[p_, e_] := (8*(p+3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 21 2023 *)
%Y Cf. A001222, A165829, A166591.
%K nonn,easy,mult
%O 1,2
%A _Jaroslav Krizek_, Nov 01 2009
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