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A336470 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336466(i) = A336466(j) and A336158(i) = A336158(j), for all i, j >= 1.

%I A336470 #7 Jul 25 2020 10:34:57
%S A336470 1,1,2,1,2,2,3,1,4,2,5,2,3,3,6,1,2,4,7,2,8,5,9,2,4,3,10,3,11,6,12,1,
%T A336470 13,2,8,4,7,7,8,2,5,8,14,5,15,9,16,2,17,4,6,3,18,10,13,3,19,11,20,6,
%U A336470 12,12,21,1,8,13,22,2,23,8,24,4,7,7,15,7,25,8,26,2,27,5,28,8,6,14,29,5,9,15,19,9,25,16,19,2,3,17,30,4,31,6,32,3,33
%N A336470 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336466(i) = A336466(j) and A336158(i) = A336158(j), for all i, j >= 1.
%C A336470 Restricted growth sequence transform of the ordered pair [A336466(n), A336158(n)].
%C A336470 For all i, j:
%C A336470   A336460(i) = A336460(j) => a(i) = a(j),
%C A336470   a(i) = a(j) => A329697(i) = A329697(j),
%C A336470   a(i) = a(j) => A336471(i) = A336471(j).
%H A336470 Antti Karttunen, <a href="/A336470/b336470.txt">Table of n, a(n) for n = 1..65537</a>
%o A336470 (PARI)
%o A336470 up_to = 65537;
%o A336470 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 A336470 A000265(n) = (n>>valuation(n,2));
%o A336470 A336466(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]-1))^f[k,2])); };
%o A336470 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A336470 A336158(n) = A046523(A000265(n));
%o A336470 Aux336470(n) = [A336466(n), A336158(n)];
%o A336470 v336470 = rgs_transform(vector(up_to, n, Aux336470(n)));
%o A336470 A336470(n) = v336470[n];
%Y A336470 Cf. A336158, A336466.
%Y A336470 Cf. also A329697, A336160, A336471.
%K A336470 nonn
%O A336470 1,3
%A A336470 _Antti Karttunen_, Jul 24 2020