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A369467 Lexicographically earliest infinite sequence such that a(i) = a(j) => A369465(i) = A369465(j) and A369465(A163511(i)) = A369465(A163511(j)), for all i, j >= 1.

%I A369467 #6 Jan 28 2024 10:52:50
%S A369467 1,1,2,1,3,2,2,1,4,3,5,2,6,2,7,1,8,4,9,3,10,5,11,2,12,6,13,2,5,7,2,1,
%T A369467 14,8,15,4,16,9,17,3,18,10,19,5,20,11,21,2,22,12,23,6,24,13,25,2,26,5,
%U A369467 27,7,11,2,28,1,29,14,30,8,31,15,32,4,33,16,34,9,35,17,36,3,37,18,38,10,39,19,40,5,41,20,42,11,43,21,44,2,45,22
%N A369467 Lexicographically earliest infinite sequence such that a(i) = a(j) => A369465(i) = A369465(j) and A369465(A163511(i)) = A369465(A163511(j)), for all i, j >= 1.
%C A369467 Restricted growth sequence transform of the ordered pair [A369458(n), A369465(n)], or equally, of the ordered pair [A369459(n), A369466(n)].
%C A369467 For all i, j >= 1: A003602(i) = A003602(j) => a(i) = a(j).
%H A369467 Antti Karttunen, <a href="/A369467/b369467.txt">Table of n, a(n) for n = 1..65537</a>
%o A369467 (PARI)
%o A369467 up_to = 65537;
%o A369467 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 A369467 A000265(n) = (n>>valuation(n,2));
%o A369467 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A369467 A163511(n) = if(!n,1,my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
%o A369467 A369465(n) = A003415(A000265(n));
%o A369467 Aux369467(n) = [A369465(n), A369465(A163511(n))];
%o A369467 v369467 = rgs_transform(vector(up_to, n, Aux369467(n)));
%o A369467 A369467(n) = v369467[n];
%Y A369467 Cf. A000265, A003415, A003602, A163511, A349905, A369458, A369459, A369465, A369466.
%K A369467 nonn
%O A369467 1,3
%A A369467 _Antti Karttunen_, Jan 28 2024