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A369457 Lexicographically earliest infinite sequence such that a(i) = a(j) => A369456(i) = A369456(j) for all i, j >= 0.

%I A369457 #8 Jan 28 2024 09:21:46
%S A369457 1,2,2,2,2,3,4,5,2,6,7,8,4,6,2,4,2,9,10,11,12,13,14,15,4,9,15,3,5,5,8,
%T A369457 3,2,14,16,7,17,18,19,19,20,21,22,23,24,18,11,6,4,15,14,6,19,25,17,14,
%U A369457 5,15,16,4,8,15,3,5,2,26,17,12,20,27,28,23,29,30,31,13,32,33,7,15,34,35,36,37,38,39,40,27,41,42,43,44,45,19
%N A369457 Lexicographically  earliest infinite sequence such that a(i) = a(j) => A369456(i) = A369456(j) for all i, j >= 0.
%C A369457 Restricted growth sequence transform of A369456.
%H A369457 Antti Karttunen, <a href="/A369457/b369457.txt">Table of n, a(n) for n = 0..65537</a>
%o A369457 (PARI)
%o A369457 up_to = 65537;
%o A369457 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 A369457 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A369457 A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
%o A369457 A369456(n) = A083345(A005940(1+n));
%o A369457 v369457 = rgs_transform(vector(1+up_to,n,A369456(n-1)));
%o A369457 A369457(n) = v369457[1+n];
%Y A369457 Cf. A005940, A083345, A369456.
%Y A369457 Cf. also A366802, A369065, A369067.
%K A369457 nonn
%O A369457 0,2
%A A369457 _Antti Karttunen_, Jan 27 2024