%I #17 Feb 01 2021 15:44:04
%S 1,2,3,6,5,30,7,42,15,10,11,210,13,14,105,462,17,330,19,390,21,22,23,
%T 2310,35,26,165,546,29,2730,31,6006,33,34,70,30030,37,38,39,46410,41,
%U 3570,43,66,1155,46,47,39270,77,770,51,78,53,4290,55,9282,57,58,59
%N Lexicographically earliest divisibility sequence consisting only of distinct squarefree numbers.
%C This sequence is a permutation of the squarefree numbers (A005117).
%H Rémy Sigrist, <a href="/A338219/b338219.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A338219/a338219.png">Colored logarithmic scatterplot of the first 100000 terms</a> (where the color is function of A001221(a(n)))
%H Rémy Sigrist, <a href="/A338219/a338219.gp.txt">PARI program for A338219</a>
%H <a href="/index/Di#divseq">Index to divisibility sequences</a>
%F a(p) = p for any prime number p.
%F a(p) < a(n) for any prime number p and n > p.
%e For n = 1:
%e - we choose a(1) = 1.
%e For n = 2:
%e - a(2) must be divisible by a(1) = 1,
%e - we choose a(2) = 2.
%e For n = 3:
%e - a(3) must be divisible by a(1) = 1,
%e - we choose a(3) = 3.
%e For n = 4:
%e - a(4) must be divisible by a(1) = 1 and a(2) = 2,
%e - we choose a(4) = 6.
%e For n = 5:
%e - a(5) must be divisible by a(1) = 1,
%e - we choose a(5) = 5.
%e For n = 6:
%e - a(6) must be divisible by a(1) = 1, a(2) = 2 and a(3) = 3,
%e - we choose a(6) = 30.
%o (PARI) See Links section.
%Y See A338461 for a similar sequence.
%Y Cf. A001221, A005117.
%K nonn,look
%O 1,2
%A _Rémy Sigrist_, Jan 30 2021