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A320013 Filter sequence constructed from the binary expansions of those proper divisors of n that are not multiples of 3.

%I A320013 #7 Oct 03 2018 21:36:53
%S A320013 1,2,2,3,2,3,2,4,2,5,2,4,2,6,7,8,2,3,2,9,10,11,2,8,7,12,2,13,2,14,2,
%T A320013 15,16,17,18,4,2,19,20,21,2,22,2,23,7,24,2,15,10,25,26,27,2,3,28,29,
%U A320013 30,31,2,32,2,33,10,34,35,36,2,37,38,39,2,8,2,40,41,42,43,44,2,45,2,46,2,47,48,49,50,51,2,14,52,53,54,55,56,34,2,57,16,58,2,59,2,60,61
%N A320013 Filter sequence constructed from the binary expansions of those proper divisors of n that are not multiples of 3.
%C A320013 Restricted growth sequence transform of ordered pair [A319991(n), A319992(n)].
%C A320013 For all i, j: a(i) = a(j) => A320015(i) = A320015(j).
%H A320013 Antti Karttunen, <a href="/A320013/b320013.txt">Table of n, a(n) for n = 1..65537</a>
%o A320013 (PARI)
%o A320013 up_to = 65537;
%o A320013 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 A320013 A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
%o A320013 A319991(n) = { my(m=1); fordiv(n,d,if((d<n)&&(1==(d%3)),m *= A019565(d))); m; };
%o A320013 A319992(n) = { my(m=1); fordiv(n,d,if((d<n)&&(2==(d%3)),m *= A019565(d))); m; };
%o A320013 v320013 = rgs_transform(vector(up_to,n,[A319991(n),A319992(n)]));
%o A320013 A320013(n) = v320013[n];
%Y A320013 Cf. A019565, A319991, A319992, A320011, A320012, A320014.
%Y A320013 Cf. also A293226, A300833.
%K A320013 nonn
%O A320013 1,2
%A A320013 _Antti Karttunen_, Oct 03 2018