%I #13 Dec 26 2019 05:35:10

%S 1,2,3,5,6,4,7,9,10,11,13,14,8,12,17,19,22,16,23,24,15,26,28,20,21,18,

%T 25,29,30,31,32,34,37,38,40,35,41,43,44,33,27,36,47,52,39,46,51,42,48,

%U 49,53,56,58,59,61,64,60,45,62,63,57,67,68,71,73,74,77

%N Lexicographically earliest sequence of distinct positive terms with an associate sequence t such that a(1) = t(1) = 1 and for n > 1, either a(n) divides t(n-1) (and in that case set t(n) = t(n-1)/a(n)) or a(n) is coprime to t(n-1) (and in that case set t(n) = t(n-1)*a(n)).

%C All prime numbers appear in the sequence, in ascending order.

%C This sequence is likely a permutation of the natural numbers.

%H Rémy Sigrist, <a href="/A330647/b330647.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A330647/a330647.png">Scatterplot of (n, a(n)-n) for n = 1..250000</a>

%H Rémy Sigrist, <a href="/A330647/a330647.gp.txt">PARI program for A330647</a>

%e The first terms, alongside the corresponding t(n), are:

%e n a(n) t(n)

%e -- ---- ----

%e 1 1 1

%e 2 2 2

%e 3 3 6

%e 4 5 30

%e 5 6 5

%e 6 4 20

%e 7 7 140

%e 8 9 1260

%e 9 10 126

%e 10 11 1386

%t Nest[Append[#1, Block[{k = 2, s}, While[Nand[FreeQ[#1[[All, 1]], k], MemberQ[{1, k}, Set[s, GCD[#3, k]]]], k++]; {k, If[s == 1, #3 k, #3/k]}]] & @@ {#, #[[-1, 1]], #[[-1, -1]]} &, {{1, 1}}, 66][[All, 1]] (* _Michael De Vlieger_, Dec 23 2019 *)

%o (PARI) See Links section.

%Y See A330648 for the corresponding sequence t.

%Y Cf. A008336.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Dec 22 2019