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A369466 Lexicographically earliest infinite sequence such that a(i) = a(j) => A369465(i) = A369465(j), for all i, j >= 1.

%I A369466 #6 Jan 27 2024 18:51:28
%S A369466 1,1,2,1,2,2,2,1,3,2,2,2,2,2,4,1,2,3,2,2,5,2,2,2,5,2,6,2,2,4,2,1,7,2,
%T A369466 8,3,2,2,9,2,2,5,2,2,10,2,2,2,7,5,11,2,2,6,9,2,12,2,2,4,2,2,13,1,14,7,
%U A369466 2,2,15,8,2,3,2,2,16,2,14,9,2,2,17,2,2,5,12,2,18,2,2,10,11,2,19,2,20,2,2,7,21,5,2,11
%N A369466 Lexicographically earliest infinite sequence such that a(i) = a(j) => A369465(i) = A369465(j), for all i, j >= 1.
%C A369466 Restricted growth sequence transform of A369465.
%C A369466 For all i, j >= 1: A003602(i) = A003602(j) => a(i) = a(j).
%H A369466 Antti Karttunen, <a href="/A369466/b369466.txt">Table of n, a(n) for n = 1..65537</a>
%o A369466 (PARI)
%o A369466 up_to = 65537;
%o A369466 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 A369466 A000265(n) = (n>>valuation(n,2));
%o A369466 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A369466 A369465(n) = A003415(A000265(n));
%o A369466 v369466 = rgs_transform(vector(up_to, n, A369465(n)));
%o A369466 A369466(n) = v369466[n];
%Y A369466 Cf. A000265, A003415, A003602, A064989, A349905, A369465.
%K A369466 nonn
%O A369466 1,3
%A A369466 _Antti Karttunen_, Jan 27 2024