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%I #12 Oct 19 2023 02:16:00
%S 1,0,9,0,27,0,45,0,81,0,81,0,99,0,243,0,135,0,153,0,405,0,189,0,729,0,
%T 729,0,243,0,261,0,729,0,1215,0,315,0,891,0,351,0,369,0,2187,0,405,0,
%U 2025,0,1215,0,459,0,2187,0,1377,0,513,0,531,0,3645,0,2673,0
%N Totally multiplicative sequence with a(p) = 9*(p-2) for prime p.
%H G. C. Greubel, <a href="/A167301/b167301.txt">Table of n, a(n) for n = 1..1000</a>
%F Multiplicative with a(p^e) = (9*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (9*(p(k)-2))^e(k).
%F a(2k) = 0 for k >= 1.
%F a(n) = A165830(n) * A166586(n) = 9^bigomega(n) * A166586(n) = 9^A001222(n) * A166586(n).
%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*9^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 07 2016 *)
%t f[p_, e_] := (9*(p-2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 19 2023 *)
%Y Cf. A001222, A165830, A166586.
%K nonn,easy,mult
%O 1,3
%A _Jaroslav Krizek_, Nov 01 2009
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