This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A366381 #10 Oct 12 2023 16:59:28
%S A366381 1,1,1,1,2,1,3,1,1,2,4,1,5,3,2,1,6,1,7,2,3,4,8,1,6,5,1,3,9,2,10,1,4,6,
%T A366381 11,1,12,7,5,2,13,3,14,4,2,8,15,1,16,6,6,5,17,1,18,3,7,9,19,2,20,10,3,
%U A366381 1,21,4,22,6,8,11,23,1,24,12,6,7,25,5,26,2,1,13,27,3,28,14,9,4,29,2,30,8,10,15,31,1,32
%N A366381 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336466(i) = A336466(j) and A336467(i) = A336467(j) for all i, j >= 1, where A336466 is fully multiplicative with a(p) = oddpart(p-1) for any prime p and A336467 is fully multiplicative with a(2) = 1 and a(p) = oddpart(p+1) for odd primes p.
%C A366381 Restricted growth sequence transform of the ordered pair [A336466(n), A336467(n)].
%C A366381 For all i, j: A003602(i) = A003602(j) => A366380(i) = A366380(j) => a(i) = a(j).
%H A366381 Antti Karttunen, <a href="/A366381/b366381.txt">Table of n, a(n) for n = 1..65537</a>
%o A366381 (PARI)
%o A366381 up_to = 65537;
%o A366381 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 A366381 A000265(n) = (n>>valuation(n,2));
%o A366381 A336466(n) = { my(f=factor(n)); prod(k=1, #f~, A000265(f[k, 1]-1)^f[k, 2]); };
%o A366381 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 A366381 A366381aux(n) = [A336466(n), A336467(n)];
%o A366381 v366381 = rgs_transform(vector(up_to,n,A366381aux(n)));
%o A366381 A366381(n) = v366381[n];
%Y A366381 Cf. A000265, A003602, A336466, A336467, A366380.
%Y A366381 Cf. also A365466, A365467.
%K A366381 nonn
%O A366381 1,5
%A A366381 _Antti Karttunen_, Oct 12 2023