%I #12 Jun 01 2022 18:09:49

%S 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 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 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 a(n) = Product_{d|n, d<n} A019565(d)^[2 == d mod 3].

%H Antti Karttunen, <a href="/A319992/b319992.txt">Table of n, a(n) for n = 1..8192</a>

%F a(n) = Product_{d|n, d<n} A019565(d)^[2 == d mod 3].

%F a(n) = A293214(n) / (A319990(n)*A319991(n)).

%F For all n >= 1:

%F A007814(a(n)) = A320005(n).

%F A048675(a(n)) = A293898(n).

%F A195017(a(n)) = -A293896(n) mod 3.

%o (PARI)

%o 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(n) = { my(m=1); fordiv(n,d,if((d<n)&&(2==(d%3)),m *= A019565(d))); m; };

%Y Cf. A019565, A293214, A293896, A293898, A319990, A319991, A320005, A320012 (rgs-transform).

%Y Cf. also A293222.

%K nonn

%O 1,4

%A _Antti Karttunen_, Oct 03 2018