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A319992 a(n) = Product_{d|n, d A019565(d)^[2 == d mod 3].

%I A319992 #12 Jun 01 2022 18:09:49
%S A319992 1,1,1,3,1,3,1,3,1,30,1,3,1,3,10,21,1,3,1,30,1,126,1,21,10,3,1,315,1,
%T A319992 30,1,21,42,66,10,3,1,3,1,11550,1,315,1,126,10,990,1,21,1,30,22,693,1,
%U A319992 3,420,2205,1,2310,1,1650,1,3,1,273,10,126,1,66,330,245700,1,21,1,3,10,585,42,693,1,11550,1,546,1,315,220,3,770
%N A319992 a(n) = Product_{d|n, d<n} A019565(d)^[2 == d mod 3].
%H A319992 Antti Karttunen, <a href="/A319992/b319992.txt">Table of n, a(n) for n = 1..8192</a>
%F A319992 a(n) = Product_{d|n, d<n} A019565(d)^[2 == d mod 3].
%F A319992 a(n) = A293214(n) / (A319990(n)*A319991(n)).
%F A319992 For all n >= 1:
%F A319992 A007814(a(n)) = A320005(n).
%F A319992 A048675(a(n)) = A293898(n).
%F A319992 A195017(a(n)) = -A293896(n) mod 3.
%o A319992 (PARI)
%o A319992 A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
%o A319992 A319992(n) = { my(m=1); fordiv(n,d,if((d<n)&&(2==(d%3)),m *= A019565(d))); m; };
%Y A319992 Cf. A019565, A293214, A293896, A293898, A319990, A319991, A320005, A320012 (rgs-transform).
%Y A319992 Cf. also A293222.
%K A319992 nonn
%O A319992 1,4
%A A319992 _Antti Karttunen_, Oct 03 2018