cp's OEIS Frontend

A320012 Filter sequence combined from those proper divisors d of n for which 2 == d (mod 3); Restricted growth sequence transform of A319992.

%I A320012 #7 Oct 03 2018 21:36:47
%S A320012 1,1,1,2,1,2,1,2,1,3,1,2,1,2,4,5,1,2,1,3,1,6,1,5,4,2,1,7,1,3,1,5,8,9,
%T A320012 4,2,1,2,1,10,1,7,1,6,4,11,1,5,1,3,12,13,1,2,14,15,1,16,1,17,1,2,1,18,
%U A320012 4,6,1,9,19,20,1,5,1,2,4,21,8,13,1,10,1,22,1,7,23,2,24,25,1,3,1,11,1,26,4,18,1,7,8,27,1,9,1,28,29
%N A320012 Filter sequence combined from those proper divisors d of n for which 2 == d (mod 3); Restricted growth sequence transform of A319992.
%C A320012 For all i, j:
%C A320012   a(i) = a(j) => A320005(i) = A320005(j),
%C A320012   a(i) = a(j) => A293898(i) = A293898(j).
%H A320012 Antti Karttunen, <a href="/A320012/b320012.txt">Table of n, a(n) for n = 1..65537</a>
%o A320012 (PARI)
%o A320012 up_to = 65537;
%o A320012 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 A320012 A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
%o A320012 A319992(n) = { my(m=1); fordiv(n,d,if((d<n)&&(2==(d%3)),m *= A019565(d))); m; };
%o A320012 v320012 = rgs_transform(vector(up_to,n,A319992(n)));
%o A320012 A320012(n) = v320012[n];
%Y A320012 Cf. A293224, A319992, A320010, A320011, A320013, A320014.
%K A320012 nonn
%O A320012 1,4
%A A320012 _Antti Karttunen_, Oct 03 2018