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 A376566 #8 Oct 01 2024 08:46:38
%S A376566 1,2,1,3,1,4,1,2,1,5,1,6,1,2,1,3,1,7,1,8,1,2,1,4,1,2,1,9,1,3,1,10,1,2,
%T A376566 1,5,1,11,1,12,1,2,1,3,1,4,1,2,1,6,1,2,1,3,1,13,1,14,1,2,1,7,1,15,1,3,
%U A376566 1,5,1,16,1,2,1,4,1,2,1,8,1,2,1,4,1,2,1
%N A376566 Lexicographically earliest sequence of positive integers such that for any n > 0, there is an even number of k's such that 1 <= k < n and a(n) divides a(k).
%C A376566 The sequence is well defined as we can always extend it with a number greater than any prior term.
%H A376566 Rémy Sigrist, <a href="/A376566/b376566.txt">Table of n, a(n) for n = 1..10000</a>
%F A376566 a(2*k-1) = 1 for any k > 0.
%F A376566 a(2*A025523(n-1)) = n for any n > 1 (and this is the first occurrence of n in the sequence). - _Hugo Pfoertner_, Oct 01 2024
%e A376566 The first terms, alongside the corresponding k's, are:
%e A376566 n a(n) k's
%e A376566 -- ---- ---------------------------------------------
%e A376566 1 1 None
%e A376566 2 2 None
%e A376566 3 1 1, 2
%e A376566 4 3 None
%e A376566 5 1 1, 2, 3, 4
%e A376566 6 4 None
%e A376566 7 1 1, 2, 3, 4, 5, 6
%e A376566 8 2 2, 6
%e A376566 9 1 1, 2, 3, 4, 5, 6, 7, 8
%e A376566 10 5 None
%e A376566 11 1 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
%e A376566 12 6 None
%e A376566 13 1 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
%e A376566 14 2 2, 6, 8, 12
%e A376566 15 1 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
%e A376566 16 3 4, 12
%o A376566 (PARI) { nb = vector(16); for (n = 1, 86, for (v = 1, oo, if (nb[v]%2==0, print1 (v ", "); fordiv (v, d, nb[d]++;); break;););); }
%Y A376566 Cf. A025523.
%K A376566 nonn
%O A376566 1,2
%A A376566 _Rémy Sigrist_, Sep 28 2024