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A366888 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366887(i) = A366887(j) for all i, j >= 0.

%I A366888 #10 Jan 03 2024 16:35:01
%S A366888 1,1,1,2,1,2,2,3,1,2,2,3,2,4,3,5,1,2,2,3,2,4,3,5,2,4,4,6,3,7,5,8,1,2,
%T A366888 2,3,2,4,3,5,2,4,4,6,3,7,5,8,2,4,4,6,4,9,6,10,3,7,7,11,5,6,8,12,1,2,2,
%U A366888 3,2,4,3,5,2,4,4,6,3,7,5,8,2,4,4,6,4,9,6,10,3,7,7,11,5,6,8,12,2,4,4,6,4,9,6,10,4,9
%N A366888 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366887(i) = A366887(j) for all i, j >= 0.
%C A366888 Restricted growth sequence transform of A366887.
%H A366888 Antti Karttunen, <a href="/A366888/b366888.txt">Table of n, a(n) for n = 0..65537</a>
%o A366888 (PARI)
%o A366888 up_to = 65537;
%o A366888 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 A366888 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 A366888 A206787(n) = sumdiv(n, d, d*issquarefree(2*d));
%o A366888 A366887(n) = A206787(A163511(n));
%o A366888 v366888 = rgs_transform(vector(1+up_to,n,A366887(n-1)));
%o A366888 A366888(n) = v366888[1+n];
%Y A366888 Cf. A163511, A206787, A366887.
%Y A366888 Cf. also A366881.
%K A366888 nonn,look
%O A366888 0,4
%A A366888 _Antti Karttunen_, Nov 04 2023