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A366880 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366879(i) = A366879(j) for all i, j >= 0.

%I A366880 #7 Oct 27 2023 16:39:56
%S A366880 1,2,3,4,3,5,6,7,3,3,7,8,3,9,10,11,3,3,3,3,3,12,13,14,3,15,16,17,3,18,
%T A366880 19,20,3,3,3,3,3,3,3,3,3,21,22,23,3,24,25,26,3,3,27,28,3,29,30,31,3,
%U A366880 32,33,34,3,17,9,25,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,35,36,3,37,38,39,3,40,41,42,3,43
%N A366880 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366879(i) = A366879(j) for all i, j >= 0.
%C A366880 Restricted growth sequence transform of A366879.
%H A366880 Antti Karttunen, <a href="/A366880/b366880.txt">Table of n, a(n) for n = 0..65537</a>
%H A366880 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%o A366880 (PARI)
%o A366880 up_to = 65537;
%o A366880 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 A366880 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 A366880 A326938(n) = sumdiv(n, d, if(n/d%2, moebius(n/d)*moebius(d)*d));
%o A366880 A366879(n) = A326938(A163511(n));
%o A366880 v366880 = rgs_transform(vector(1+up_to,n,A366879(n-1)));
%o A366880 A366880(n) = v366880[1+n];
%Y A366880 Cf. A002131, A163511, A326938, A366879.
%Y A366880 Cf. also A366878.
%K A366880 nonn
%O A366880 0,2
%A A366880 _Antti Karttunen_, Oct 27 2023