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%I #10 Aug 10 2020 09:29:46
%S 1,1,2,1,3,2,4,1,2,3,5,2,6,4,7,1,8,2,9,3,10,5,11,2,12,6,2,4,13,7,14,1,
%T 15,8,16,2,17,9,18,3,19,10,20,5,7,11,21,2,4,12,22,6,23,2,24,4,25,13,
%U 26,7,27,14,10,1,28,15,29,8,30,16,31,2,32,17,33,9,34,18,35,3,2,19,36,10,37,20,38,5,39,7,18,11,40,21,41,2,42,4,15,12
%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A336467(i) = A336467(j) and A278221(A000265(i)) = A278221(A000265(j)), for all i, j >= 1.
%C Restricted growth sequence transform of the ordered pair [A336467(n), A278221(A000265(n))], or equally, of the ordered pair [A336467(n), A336395(n)].
%C For all i, j:
%C A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j).
%H Antti Karttunen, <a href="/A336393/b336393.txt">Table of n, a(n) for n = 1..65537</a>
%o (PARI)
%o up_to = 65537;
%o 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 A000265(n) = (n>>valuation(n,2));
%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A122111(n) = if(1==n,n,my(f=factor(n), es=Vecrev(f[,2]),is=concat(apply(primepi,Vecrev(f[,1])),[0]),pri=0,m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
%o A278221(n) = A046523(A122111(n));
%o 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 Aux336393(n) = [A336467(n), A278221(A000265(n))];
%o v336393 = rgs_transform(vector(up_to, n, Aux336393(n)));
%o A336393(n) = v336393[n];
%Y Cf. A000265, A003602, A324400, A278221, A286621, A336390, A336395, A336467.
%K nonn
%O 1,3
%A _Antti Karttunen_, Aug 10 2020
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