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A336390 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336467(i) = A336467(j) and A336158(i) = A336158(j), for all i, j >= 1.

%I A336390 #6 Aug 10 2020 09:29:09
%S A336390 1,1,2,1,3,2,2,1,4,3,3,2,5,2,6,1,7,4,8,3,9,3,3,2,10,5,11,2,12,6,2,1,6,
%T A336390 7,6,4,13,8,14,3,15,9,16,3,17,3,3,2,4,10,18,5,19,11,18,2,20,12,12,6,
%U A336390 21,2,22,1,23,6,24,7,6,6,7,4,25,13,26,8,6,14,8,3,27,15,15,9,28,16,29,3,30,17,14,3,9,3,29,2,31,4,17,10,32,18,33,5,34
%N A336390 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336467(i) = A336467(j) and A336158(i) = A336158(j), for all i, j >= 1.
%C A336390 Restricted growth sequence transform of the ordered pair [A336467(n), A336158(n)].
%C A336390 For all i, j:
%C A336390   A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j),
%C A336390   a(i) = a(j) => A331410(i) = A331410(j),
%C A336390   a(i) = a(j) => A336391(i) = A336391(j).
%H A336390 Antti Karttunen, <a href="/A336390/b336390.txt">Table of n, a(n) for n = 1..65537</a>
%o A336390 (PARI)
%o A336390 up_to = 65537;
%o A336390 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 A336390 A000265(n) = (n>>valuation(n,2));
%o A336390 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A336390 A336158(n) = A046523(A000265(n));
%o A336390 A336467(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]+1))^f[k,2])); };
%o A336390 Aux336390(n) = [A336158(n), A336467(n)];
%o A336390 v336390 = rgs_transform(vector(up_to, n, Aux336390(n)));
%o A336390 A336390(n) = v336390[n];
%Y A336390 Cf. A003602, A324400, A336158, A336467, A336391, A336393.
%Y A336390 Cf. also A336470.
%K A336390 nonn
%O A336390 1,3
%A A336390 _Antti Karttunen_, Aug 10 2020