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A372569 Lexicographically earliest infinite sequence such that a(i) = a(j) => A009194(i) = A009194(j), A009195(i) = A009195(j) and A009223(i) = A009223(j), for all i, j >= 1.

%I A372569 #6 May 25 2024 16:59:45
%S A372569 1,1,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,7,2,15,16,9,17,18,2,
%T A372569 19,2,20,21,7,22,23,2,9,24,25,2,26,2,8,27,7,2,28,29,30,10,13,2,31,32,
%U A372569 33,14,7,2,34,2,9,35,36,37,38,2,13,21,39,2,40,2,9,41,8,37,42,2,43,44,7,2,45,46,9,10,47,2,48,49,8,14,7,50,51,2,52,53,54,2,19,2
%N A372569 Lexicographically earliest infinite sequence such that a(i) = a(j) => A009194(i) = A009194(j), A009195(i) = A009195(j) and A009223(i) = A009223(j), for all i, j >= 1.
%C A372569 Restricted growth sequence transform of the triple [A009194(n), A009195(n), A009223(n)].
%C A372569 For all i, j: A372570(i) = A372570(j) => a(i) = a(j) => A074389(i) = A074389(j).
%H A372569 Antti Karttunen, <a href="/A372569/b372569.txt">Table of n, a(n) for n = 1..65537</a>
%o A372569 (PARI)
%o A372569 up_to = 65537;
%o A372569 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 A372569 Aux372569(n) = [gcd(n, sigma(n)), gcd(n, eulerphi(n)), gcd(eulerphi(n), sigma(n))];
%o A372569 v372569 = rgs_transform(vector(up_to, n, Aux372569(n)));
%o A372569 A372569(n) = v372569[n];
%Y A372569 Cf. A009194, A009195, A009223.
%Y A372569 Cf. also A372570, A372572.
%K A372569 nonn
%O A372569 1,3
%A A372569 _Antti Karttunen_, May 25 2024