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A366895 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366894(i) = A366894(j) for all i, j >= 0.

%I A366895 #10 Aug 04 2025 09:02:12
%S A366895 1,1,1,1,1,2,1,1,1,3,2,1,1,1,1,1,1,4,3,5,2,1,1,6,1,5,1,1,1,1,1,1,1,7,
%T A366895 4,8,3,5,5,9,2,10,1,11,1,6,6,12,1,1,5,1,1,1,1,1,1,2,1,5,1,1,1,1,1,13,
%U A366895 7,14,4,8,8,15,3,16,5,17,5,9,9,7,2,18,10,19,1,11,11,12,1,20,6,21,6,12,12,7,1,22,1,5,5
%N A366895 Lexicographically  earliest infinite sequence such that a(i) = a(j) => A366894(i) = A366894(j) for all i, j >= 0.
%C A366895 Restricted growth sequence transform of A366894.
%C A366895 For all i, j >= 0:
%C A366895   A366881(i) = A366881(j) => A366806(i) = A366806(j) => a(i) = a(j).
%H A366895 Antti Karttunen, <a href="/A366895/b366895.txt">Table of n, a(n) for n = 0..65537</a>
%o A366895 (PARI)
%o A366895 up_to = 65537;
%o A366895 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 A366895 A000265(n) = (n>>valuation(n,2));
%o A366895 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 A366895 A336699(n) = A000265(1+A000265(sigma(A000265(n))));
%o A366895 A366894(n) = A336699(A163511(n));
%o A366895 v366895 = rgs_transform(vector(1+up_to,n,A366894(n-1)));
%o A366895 A366895(n) = v366895[1+n];
%Y A366895 Cf. A000265, A000593, A163511, A324186, A336699, A351565, A366894.
%Y A366895 Cf. also A366806, A366881.
%K A366895 nonn,look
%O A366895 0,6
%A A366895 _Antti Karttunen_, Jan 03 2024