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%I #7 Oct 03 2018 21:36:40
%S 1,2,2,2,2,2,2,3,2,2,2,3,2,4,2,3,2,2,2,5,4,2,2,3,2,6,2,7,2,8,2,9,2,2,
%T 4,3,2,10,6,5,2,4,2,11,2,2,2,9,4,12,2,13,2,2,2,14,10,2,2,5,2,15,4,9,6,
%U 16,2,17,2,18,2,3,2,19,20,21,4,6,2,22,2,2,2,14,2,23,2,11,2,8,24,25,15,2,10,9,2,26,2,27,2,28,2,29,4
%N Filter sequence combined from those proper divisors d of n for which +1 == d (mod 3); Restricted growth sequence transform of A319991.
%C For all i, j:
%C a(i) = a(j) => A320001(i) = A320001(j),
%C a(i) = a(j) => A293897(i) = A293897(j).
%H Antti Karttunen, <a href="/A320011/b320011.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 A319991(n) = { my(m=1); fordiv(n,d,if((d<n)&&(1==(d%3)),m *= A019565(d))); m; };
%o v320011 = rgs_transform(vector(up_to,n,A319991(n)));
%o A320011(n) = v320011[n];
%Y Cf. A293223, A319991, A320010, A320012, A320013, A320014.
%K nonn
%O 1,2
%A _Antti Karttunen_, Oct 03 2018
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