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A336392 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A336467(i) = A336467(j), for all i, j >= 1.

%I A336392 #7 Aug 10 2020 09:29:38
%S A336392 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 A336392 1,3,9,6,5,17,10,18,3,19,11,20,6,21,12,22,2,23,13,24,7,25,14,26,4,27,
%U A336392 15,28,8,29,16,30,1,31,3,32,9,33,6,34,5,35,17,36,10,21,18,37,3,11,19,38,11,39,20,40,6,41,21,42,12,43,22,44,2,45,23,46,13
%N A336392 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A336467(i) = A336467(j), for all i, j >= 1.
%C A336392 Restricted growth sequence transform of the ordered pair [A278222(n), A336467(n)].
%C A336392 For all i, j:  A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j).
%H A336392 Antti Karttunen, <a href="/A336392/b336392.txt">Table of n, a(n) for n = 1..65537</a>
%o A336392 (PARI)
%o A336392 up_to = 65537;
%o A336392 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 A336392 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A336392 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A336392 A278222(n) = A046523(A005940(1+n));
%o A336392 A000265(n) = (n>>valuation(n,2));
%o A336392 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 A336392 Aux336392(n) = [A278222(n), A336467(n)];
%o A336392 v336392 = rgs_transform(vector(up_to, n, Aux336392(n)));
%o A336392 A336392(n) = v336392[n];
%Y A336392 Cf. A003602, A278222, A324400, A336390, A336391, A336394, A336467.
%Y A336392 Cf. also A286622, A336472.
%K A336392 nonn
%O A336392 1,3
%A A336392 _Antti Karttunen_, Aug 10 2020