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A319990 a(n) = Product_{d|n, d A019565(d)^[0 == d mod 3].

%I A319990 #9 Oct 03 2018 21:36:11
%S A319990 1,1,1,1,1,6,1,1,6,1,1,90,1,1,6,1,1,1260,1,1,6,1,1,3150,1,1,84,1,1,
%T A319990 18900,1,1,6,1,1,1455300,1,1,6,1,1,9900,1,1,17640,1,1,242550,1,1,6,1,
%U A319990 1,19209960,1,1,6,1,1,764032500,1,1,9240,1,1,2340,1,1,6,1,1,7283776500,1,1,1260,1,1,35100,1,1,38808,1,1,94594500,1,1,6,1,1
%N A319990 a(n) = Product_{d|n, d<n} A019565(d)^[0 == d mod 3].
%H A319990 Antti Karttunen, <a href="/A319990/b319990.txt">Table of n, a(n) for n = 1..8192</a>
%F A319990 a(n) = Product_{d|n, d<n} A019565(d)^[0 == d mod 3].
%F A319990 a(n) = A293214(n) / (A319991(n)*A319992(n)).
%F A319990 For all n >= 1:
%F A319990 A007814(a(n)) = A320003(n).
%F A319990 A195017(a(n)) = 0 mod 3.
%o A319990 (PARI)
%o A319990 A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
%o A319990 A319990(n) = { my(m=1); fordiv(n,d,if((d<n)&&(0==(d%3)),m *= A019565(d))); m; };
%Y A319990 Cf. A293214, A319991, A319992, A320003, A320010 (rgs-transform).
%K A319990 nonn
%O A319990 1,6
%A A319990 _Antti Karttunen_, Oct 03 2018