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%I #11 Oct 22 2023 00:49:55
%S 1,-9,0,81,18,0,36,-729,0,-162,72,0,90,-324,0,6561,126,0,144,1458,0,
%T -648,180,0,324,-810,0,2916,234,0,252,-59049,0,-1134,648,0,306,-1296,
%U 0,-13122,342,0,360,5832,0,-1620,396,0,1296,-2916,0,7290,450,0,1296,-26244
%N Totally multiplicative sequence with a(p) = 9*(p-3) for prime p.
%H G. C. Greubel, <a href="/A167319/b167319.txt">Table of n, a(n) for n = 1..1000</a>
%F Multiplicative with a(p^e) = (9*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (9*(p(k)-3))^e(k).
%F a(3k) = 0 for k >= 1.
%F a(n) = A165830(n) * A166589(n) = 9^bigomega(n) * A166589(n) = 9^A001222(n) * A166589(n).
%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*9^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 09 2016 *)
%t f[p_, e_] := (9*(p-3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 22 2023 *)
%Y Cf. A001222, A165830, A166589.
%K sign,easy,mult
%O 1,2
%A _Jaroslav Krizek_, Nov 01 2009
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