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%I #13 Jan 30 2022 09:51:58
%S 1,1,2,1,3,2,4,1,5,3,6,2,6,4,7,1,3,5,8,3,9,6,10,2,6,6,11,4,10,7,12,1,
%T 13,3,8,5,9,8,10,3,14,9,15,6,16,10,17,2,18,6,19,6,16,11,20,4,21,10,22,
%U 7,23,12,24,1,13,13,18,3,25,8,21,5,9,9,16,8,15,10,17,3,25,14,16,9,26,15,27,6,16,16,28,10,27,17,29,2,6,18,30,6,16,19,20,6,15
%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A329697(i) = A329697(j), for all i, j >= 1.
%C Restricted growth sequence transform of the ordered pair [A278222(n), A329697(n)].
%C For all i, j: A336460(i) = A336460(j) => a(i) = a(j).
%H Antti Karttunen, <a href="/A336473/b336473.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 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A278222(n) = A046523(A005940(1+n));
%o A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
%o Aux336473(n) = [A278222(n), A329697(n)];
%o v336473 = rgs_transform(vector(up_to, n, Aux336473(n)));
%o A336473(n) = v336473[n];
%Y Cf. A278222, A329697.
%Y Cf. also A286622, A336394, A336460, A336470, A336471, A336472, A336474.
%K nonn,look
%O 1,3
%A _Antti Karttunen_, Jul 24 2020
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