%I #12 Oct 19 2023 02:16:57
%S 1,32,40,1024,56,1280,72,32768,1600,1792,104,40960,120,2304,2240,
%T 1048576,152,51200,168,57344,2880,3328,200,1310720,3136,3840,64000,
%U 73728,248,71680,264,33554432,4160,4864,4032,1638400,312,5376,4800,1835008,344,92160,360
%N Totally multiplicative sequence with a(p) = 8*(p+2) for prime p.
%H G. C. Greubel, <a href="/A167309/b167309.txt">Table of n, a(n) for n = 1..1000</a>
%F Multiplicative with a(p^e) = (8*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (8*(p(k)+2))^e(k).
%F a(n) = A165829(n) * A166590(n) = 8^bigomega(n) * A166590(n) = 8^A001222(n) * A166590(n).
%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 2)^fi[[All, 2]])); Table[a[n]*8^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 07 2016 *)
%t f[p_, e_] := (8*(p+2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 19 2023 *)
%Y Cf. A001222, A165829, A166590.
%K nonn,easy,mult
%O 1,2
%A _Jaroslav Krizek_, Nov 01 2009