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A324389 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A009194(n), A318458(n)] for all other numbers, except f(1) = -1.

%I A324389 #15 Feb 04 2020 21:44:12
%S A324389 1,2,3,2,3,4,3,2,2,5,3,6,3,7,8,2,3,9,3,10,3,11,3,12,2,13,14,15,3,16,3,
%T A324389 2,17,18,3,19,3,11,3,20,3,21,3,22,23,7,3,6,2,24,25,26,3,27,28,29,28,
%U A324389 30,3,31,3,32,33,2,3,34,3,18,17,35,3,36,3,5,3,37,3,38,3,39,2,18,3,40,41,11,17,42,3,43,44,45,3,46,47,12,3,48,23,49,3,50,3
%N A324389 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A009194(n), A318458(n)] for all other numbers, except f(1) = -1.
%C A324389 For all i, j:
%C A324389   A324401(i) = A324401(j) => a(i) = a(j).
%C A324389 Regarding the scatter plot of this sequence, see also comments in A318310. - _Antti Karttunen_, Feb 04 2020
%H A324389 Antti Karttunen, <a href="/A324389/b324389.txt">Table of n, a(n) for n = 1..65537</a>
%H A324389 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A324389 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A324389 (PARI)
%o A324389 up_to = 65537;
%o A324389 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 A324389 A009194(n) = gcd(n,sigma(n));
%o A324389 A318458(n) = bitand(n,sigma(n)-n);
%o A324389 Aux324389(n) = if(1==n,-1,[A009194(n), A318458(n)]);
%o A324389 v324389 = rgs_transform(vector(up_to,n,Aux324389(n)));
%o A324389 A324389(n) = v324389[n];
%Y A324389 Cf. A009194, A318310, A318458, A324390, A324401, A324530, A331744, A331746, A331747.
%K A324389 nonn,look
%O A324389 1,2
%A A324389 _Antti Karttunen_, Mar 05 2019