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A331746 Lexicographically earliest infinite sequence such that a(i) = a(j) => A009194(i) = A009194(j) and A331166(i) = A331166(j) for all i, j.

%I A331746 #6 Feb 04 2020 21:44:40
%S A331746 1,2,3,4,5,6,7,8,9,10,11,12,11,13,14,15,16,17,18,19,20,21,22,23,18,21,
%T A331746 24,25,22,26,27,28,29,30,31,32,33,34,35,36,33,37,38,39,40,41,42,43,31,
%U A331746 44,45,46,38,47,48,49,35,41,48,50,42,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,63,71,72,73,74,75,76,66,77,78,79,80,81,82,83,56
%N A331746 Lexicographically earliest infinite sequence such that a(i) = a(j) => A009194(i) = A009194(j) and A331166(i) = A331166(j) for all i, j.
%C A331746 Restricted growth sequence transform of the ordered pair [A009194(n), A331166(n)].
%C A331746 For all i, j:
%C A331746    a(i) = a(j) => A331747(i) = A331747(j).
%H A331746 Antti Karttunen, <a href="/A331746/b331746.txt">Table of n, a(n) for n = 1..65537</a>
%H A331746 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A331746 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A331746 (PARI)
%o A331746 \\ Needs also code from A331166.
%o A331746 up_to = 65537;
%o A331746 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 A331746 A009194(n) = gcd(n, sigma(n));
%o A331746 Aux331746(n) = [A009194(n),A331166(n)];
%o A331746 v331746 = rgs_transform(vector(up_to, n, Aux331746(n)));
%o A331746 A331746(n) = v331746[n];
%Y A331746 Cf. A009194, A331166, A331300.
%Y A331746 Cf. also A331744, A331747.
%K A331746 nonn
%O A331746 1,2
%A A331746 _Antti Karttunen_, Feb 04 2020