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a(n) = Product_{d|n, d<n} A019565(d)^[1 == d mod 3].
8

%I #9 Oct 03 2018 21:36:18

%S 1,2,2,2,2,2,2,10,2,2,2,10,2,60,2,10,2,2,2,210,60,2,2,10,2,140,2,300,

%T 2,42,2,110,2,2,60,10,2,132,140,210,2,60,2,1650,2,2,2,110,60,6468,2,

%U 700,2,2,2,115500,132,2,2,210,2,4620,60,110,140,330,2,390,2,1260,2,10,2,260,308,660,60,140,2,210210,2,2,2,115500,2,1092,2

%N a(n) = Product_{d|n, d<n} A019565(d)^[1 == d mod 3].

%H Antti Karttunen, <a href="/A319991/b319991.txt">Table of n, a(n) for n = 1..8192</a>

%F a(n) = Product_{d|n, d<n} A019565(d)^[1 == d mod 3].

%F a(n) = A293214(n) / (A319990(n)*A319992(n)).

%F For all n >= 1:

%F A007814(a(n)) = A320001(n).

%F A048675(a(n)) = A293897(n).

%F A195017(a(n)) = A293895(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]])~))}; \\ This function from _M. F. Hasler_

%o A319991(n) = { my(m=1); fordiv(n,d,if((d<n)&&(1==(d%3)),m *= A019565(d))); m; };

%Y Cf. A019565, A293214, A293895, A293897, A319990, A319992, A320001, A320011 (rgs-transform).

%Y Cf. also A293221.

%K nonn

%O 1,2

%A _Antti Karttunen_, Oct 03 2018