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A369050 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(1) = 1, and for n>1, f(n) = [A003415(n), A369049(n)], for all i, j >= 1.

%I A369050 #9 Jan 15 2024 19:19:04
%S A369050 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,17,18,19,20,2,
%T A369050 21,2,22,23,24,25,26,2,27,28,29,2,30,2,31,32,33,2,34,35,36,37,38,2,39,
%U A369050 28,40,41,42,2,43,2,44,45,46,47,48,2,49,50,51,2,52,2,53,54,55,56,57,2,58,59,60,2,61,62,63,64,65,2,66,37
%N A369050 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(1) = 1, and for n>1, f(n) = [A003415(n), A369049(n)], for all i, j >= 1.
%C A369050 Restricted growth sequence transform of the function f defined as: f(1) = 1, and for n>1, f(n) = [A003415(n), A369049(n)].
%C A369050 For all i, j:
%C A369050   A305800(i) = A305800(j) => a(i) = a(j),
%C A369050   a(i) = a(j) => A344025(i) = A344025(j) => A369051(i) = A369051(j).
%H A369050 Antti Karttunen, <a href="/A369050/b369050.txt">Table of n, a(n) for n = 1..100000</a>
%o A369050 (PARI)
%o A369050 up_to = 65537;
%o A369050 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 A369050 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A369050 A369049(n) = (n % A003415(n));
%o A369050 Aux369050(n) = if(1==n,1,[A003415(n), A369049(n)]);
%o A369050 v369050 = rgs_transform(vector(up_to, n, Aux369050(n)));
%o A369050 A369050(n) = v369050[n];
%Y A369050 Cf. A003415, A369049.
%Y A369050 Cf. also A305800, A328767, A344025, A369051.
%Y A369050 Differs from A351260 for the first time at n=77, where a(77) = 56, while A351260(77) = 47.
%Y A369050 Differs from A300833 for the first time at n=91, where a(91) = 37, while A300833(91) = 67.
%K A369050 nonn
%O A369050 1,2
%A A369050 _Antti Karttunen_, Jan 15 2024