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A369459 Lexicographically earliest infinite sequence such that a(i) = a(j) => A369458(i) = A369458(j) for all i, j >= 0.

%I A369459 #9 Jan 28 2024 10:52:41
%S A369459 1,1,1,2,1,3,2,2,1,4,3,5,2,6,2,2,1,7,4,8,3,9,5,10,2,11,6,12,2,5,2,2,1,
%T A369459 13,7,14,4,15,8,16,3,17,9,18,5,19,10,20,2,21,11,22,6,23,12,24,2,25,5,
%U A369459 26,2,10,2,2,1,27,13,28,7,29,14,30,4,31,15,32,8,33,16,34,3,35,17,36,9,37,18,38,5,39,19,40,10,41,20,42,2
%N A369459 Lexicographically earliest infinite sequence such that a(i) = a(j) => A369458(i) = A369458(j) for all i, j >= 0.
%C A369459 Restricted growth sequence transform of A369458.
%C A369459 For all i, j >= 1:
%C A369459   A003602(i) = A003602(j) => A369467(i) = A369467(j) => a(i) = a(j).
%H A369459 Antti Karttunen, <a href="/A369459/b369459.txt">Table of n, a(n) for n = 0..65537</a>
%F A369459 For all n > 0, a(n) = a(2*n) = a(A000265(n)).
%o A369459 (PARI)
%o A369459 up_to = 65537;
%o A369459 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 A369459 A000265(n) = (n>>valuation(n,2));
%o A369459 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A369459 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 A369459 A369458(n) = A003415(A000265(A163511(n)));
%o A369459 v369459 = rgs_transform(vector(1+up_to,n,A369458(n-1)));
%o A369459 A369459(n) = v369459[1+n];
%Y A369459 Cf. A000265, A003415, A003602, A163511, A369458, A369465, A369467.
%Y A369459 Cf. also A369065.
%K A369459 nonn
%O A369459 0,4
%A A369459 _Antti Karttunen_, Jan 28 2024