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A336472 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A336466(i) = A336466(j), for all i, j >= 1.

%I A336472 #7 Jul 25 2020 10:36:41
%S A336472 1,1,2,1,3,2,4,1,3,3,5,2,6,4,7,1,3,3,8,3,9,5,10,2,11,6,12,4,13,7,14,1,
%T A336472 15,3,6,3,16,8,17,3,18,9,19,5,20,10,21,2,8,11,12,6,22,12,23,4,24,13,
%U A336472 25,7,26,14,27,1,28,15,29,3,30,6,31,3,16,16,20,8,32,17,33,3,34,18,35,9,36,19,37,5,38,20,39,10,40,21,41,2,6,8,42,11,43,12,44,6,45
%N A336472 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A336466(i) = A336466(j), for all i, j >= 1.
%C A336472 Restricted growth sequence transform of the ordered pair [A278222(n), A336466(n)].
%C A336472 For all i, j: A336460(i) = A336460(j) => a(i) = a(j).
%H A336472 Antti Karttunen, <a href="/A336472/b336472.txt">Table of n, a(n) for n = 1..65537</a>
%o A336472 (PARI)
%o A336472 up_to = 65537;
%o A336472 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 A336472 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A336472 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A336472 A278222(n) = A046523(A005940(1+n));
%o A336472 A000265(n) = (n>>valuation(n,2));
%o A336472 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 A336472 Aux336472(n) = [A278222(n), A336466(n)];
%o A336472 v336472 = rgs_transform(vector(up_to, n, Aux336472(n)));
%o A336472 A336472(n) = v336472[n];
%Y A336472 Cf. A278222, A336466.
%Y A336472 Cf. also A336162, A336460, A336470, A336471, A336473.
%K A336472 nonn
%O A336472 1,3
%A A336472 _Antti Karttunen_, Jul 24 2020