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A331744 Lexicographically earliest infinite sequence such that a(i) = a(j) => A009194(i) = A009194(j) and A323901(i) = A323901(j) for all i, j.

%I A331744 #10 Feb 04 2020 21:44:22
%S A331744 1,1,2,1,3,4,5,1,6,7,8,9,3,10,11,1,12,13,14,7,15,16,17,18,19,7,17,20,
%T A331744 6,21,22,1,23,24,25,6,26,27,28,29,30,31,32,33,34,35,36,9,30,19,37,7,
%U A331744 15,38,39,40,41,42,14,43,41,44,22,1,45,46,47,24,48,49,50,13,51,52,53,54,55,56,57,7,58,59,60,61,62,63,64,33,65,66,67,68,69,70,71,18,69,30,72,19
%N A331744 Lexicographically earliest infinite sequence such that a(i) = a(j) => A009194(i) = A009194(j) and A323901(i) = A323901(j) for all i, j.
%C A331744 Restricted growth sequence transform of the ordered pair [A009194(n), A323901(n)].
%H A331744 Antti Karttunen, <a href="/A331744/b331744.txt">Table of n, a(n) for n = 1..65537</a>
%H A331744 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A331744 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%H A331744 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%F A331744 a(2^n) = 1 for all n >= 0.
%o A331744 (PARI)
%o A331744 \\ Needs also code from A323901.
%o A331744 up_to = 65537;
%o A331744 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 A331744 A009194(n) = gcd(n, sigma(n));
%o A331744 Aux331744(n) = [A009194(n),A323901(n)];
%o A331744 v331744 = rgs_transform(vector(up_to, n, Aux331744(n)));
%o A331744 A331744(n) = v331744[n];
%Y A331744 Cf. A002487, A009194, A163511, A323901.
%Y A331744 Cf. also A324400, A318310, A324389, A331745, A331746, A331747.
%K A331744 nonn
%O A331744 1,3
%A A331744 _Antti Karttunen_, Feb 04 2020