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A365391 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336158(i) = A336158(j) and A365425(i) = A365425(j) for all i, j >= 1.

%I A365391 #14 Jan 03 2024 16:33:48
%S A365391 1,1,2,1,3,2,2,1,4,3,3,2,5,2,6,1,7,4,8,3,9,3,3,2,10,5,11,2,5,6,2,1,12,
%T A365391 7,13,4,14,8,15,3,16,9,17,3,18,3,3,2,19,10,9,5,20,11,21,2,9,5,5,6,5,2,
%U A365391 22,1,23,12,24,7,25,13,7,4,26,14,27,8,28,15,8,3,29,16,16,9,30,17,9,3,16,18,9,3,9,3,31,2
%N A365391 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336158(i) = A336158(j) and A365425(i) = A365425(j) for all i, j >= 1.
%C A365391 Restricted growth sequence transform of the ordered pair [A336158(n), A365425(n)].
%C A365391 For all i, j:
%C A365391   A003602(i) = A003602(j) => a(i) = a(j),
%C A365391   A365392(i) = A365392(j) => a(i) = a(j).
%H A365391 Antti Karttunen, <a href="/A365391/b365391.txt">Table of n, a(n) for n = 1..65537</a>
%o A365391 (PARI)
%o A365391 up_to = 65537;
%o A365391 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 A365391 A000265(n) = (n>>valuation(n,2));
%o A365391 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A365391 A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
%o A365391 A365391aux(n) = [A046523(A000265(n)), A046523(A000265(A163511(n)))];
%o A365391 v365391 = rgs_transform(vector(up_to,n,A365391aux(n)));
%o A365391 A365391(n) = v365391[n];
%Y A365391 Cf. A000265, A003602, A046523, A163511, A336158, A365425, A365392.
%Y A365391 Cf. also A286531, A336159.
%K A365391 nonn,look
%O A365391 1,3
%A A365391 _Antti Karttunen_, Sep 03 2023