%I #12 Oct 22 2023 00:51:22
%S 1,15,18,225,24,270,30,3375,324,360,42,4050,48,450,432,50625,60,4860,
%T 66,5400,540,630,78,60750,576,720,5832,6750,96,6480,102,759375,756,
%U 900,720,72900,120,990,864,81000,132,8100,138,9450,7776,1170,150,911250,900
%N Totally multiplicative sequence with a(p) = 3*(p+3) for prime p.
%H G. C. Greubel, <a href="/A167322/b167322.txt">Table of n, a(n) for n = 1..1000</a>
%F Multiplicative with a(p^e) = (3*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (3*(p(k)+3))^e(k).
%F a(n) = A165824(n) * A166591(n) = 3^bigomega(n) * A166591(n) = 3^A001222(n) * A166591(n).
%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*3^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 09 2016 *)
%t f[p_, e_] := (3*(p+3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 22 2023 *)
%Y Cf. A001222, A165824, A166591.
%K nonn,easy,mult
%O 1,2
%A _Jaroslav Krizek_, Nov 01 2009
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