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Lexicographically earliest divisibility sequence consisting only of distinct squarefree numbers.
2

%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