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A336394 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A331410(i) = A331410(j), for all i, j >= 1.

%I A336394 #9 Jan 30 2022 09:51:52
%S A336394 1,1,2,1,3,2,4,1,3,3,5,2,5,4,6,1,7,3,8,3,9,5,10,2,11,5,12,4,13,6,14,1,
%T A336394 7,7,8,3,15,8,16,3,17,9,18,5,19,10,20,2,5,11,21,5,19,12,22,4,13,13,22,
%U A336394 6,20,14,23,1,24,7,11,7,17,8,16,3,25,15,26,8,18,16,27,3,15,17,18,9,28,18,29,5,26,19,30,10,31,20,32,2,8,5,21,11
%N A336394 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A331410(i) = A331410(j), for all i, j >= 1.
%C A336394 Restricted growth sequence transform of the ordered pair [A278222(n), A331410(n)].
%C A336394 For all i, j: A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j).
%H A336394 Antti Karttunen, <a href="/A336394/b336394.txt">Table of n, a(n) for n = 1..65537</a>
%o A336394 (PARI)
%o A336394 up_to = 65537;
%o A336394 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 A336394 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A336394 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A336394 A278222(n) = A046523(A005940(1+n));
%o A336394 A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));
%o A336394 Aux336394(n) = [A278222(n), A331410(n)];
%o A336394 v336394 = rgs_transform(vector(up_to, n, Aux336394(n)));
%o A336394 A336394(n) = v336394[n];
%Y A336394 Cf. A003602, A278222, A324400, A331410, A336392.
%Y A336394 Cf. also A286622, A336473.
%K A336394 nonn,look
%O A336394 1,3
%A A336394 _Antti Karttunen_, Aug 10 2020