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A336934 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007733(i) = A007733(j) and A336158(i) = A336158(j), for all i, j >= 1.

%I A336934 #5 Aug 10 2020 22:19:47
%S A336934 1,1,2,1,3,2,4,1,5,3,6,2,7,4,8,1,9,5,10,3,11,6,12,2,13,7,14,4,15,8,16,
%T A336934 1,17,9,18,5,19,10,18,3,20,11,21,6,22,12,23,2,24,13,25,7,26,14,27,4,
%U A336934 28,15,29,8,30,16,31,1,18,17,32,9,33,18,34,5,35,19,36,10,37,18,38,3,39,20,40,11,25,21,41,6,12,22,18,12,17,23,42,2,43,24,44,13,45,25,46,7,47
%N A336934 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007733(i) = A007733(j) and A336158(i) = A336158(j), for all i, j >= 1.
%C A336934 Restricted growth sequence transform of the ordered pair [A007733(n), A336158(n)].
%C A336934 For all i, j: A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j).
%H A336934 Antti Karttunen, <a href="/A336934/b336934.txt">Table of n, a(n) for n = 1..65537</a>
%o A336934 (PARI)
%o A336934 up_to = 65537;
%o A336934 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 A336934 A007733(n) = znorder(Mod(2, n/2^valuation(n, 2))); \\ From A007733
%o A336934 A000265(n) = (n>>valuation(n,2));
%o A336934 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A336934 A336158(n) = A046523(A000265(n));
%o A336934 Aux336934(n) = [A007733(n), A336158(n)];
%o A336934 v336934 = rgs_transform(vector(up_to, n, Aux336934(n)));
%o A336934 A336934(n) = v336934[n];
%Y A336934 Cf. A007733, A336158, A336933, A336935, A336936.
%K A336934 nonn
%O A336934 1,3
%A A336934 _Antti Karttunen_, Aug 10 2020