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%I #7 Oct 03 2018 21:36:33
%S 1,1,1,1,1,2,1,1,2,1,1,3,1,1,2,1,1,4,1,1,2,1,1,5,1,1,6,1,1,7,1,1,2,1,
%T 1,8,1,1,2,1,1,9,1,1,10,1,1,11,1,1,2,1,1,12,1,1,2,1,1,13,1,1,14,1,1,
%U 15,1,1,2,1,1,16,1,1,4,1,1,17,1,1,18,1,1,19,1,1,2,1,1,20,1,1,2,1,1,21,1,1,22,1,1,23,1,1,24
%N Filter sequence combined from those proper divisors of n that are multiples of 3; Restricted growth sequence transform of A319990.
%C For all i, j: a(i) = a(j) => A320003(i) = A320003(j).
%H Antti Karttunen, <a href="/A320010/b320010.txt">Table of n, a(n) for n = 1..65537</a>
%o (PARI)
%o up_to = 65537;
%o rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
%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 A319990(n) = { my(m=1); fordiv(n,d,if((d<n)&&(0==(d%3)),m *= A019565(d))); m; };
%o v320010 = rgs_transform(vector(up_to,n,A319990(n)));
%o A320010(n) = v320010[n];
%Y Cf. A319990, A320011, A320012, A320014.
%K nonn
%O 1,6
%A _Antti Karttunen_, Oct 03 2018
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