A377151 - OEIS

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A377151

Lexicographically earliest sequence of distinct positive integers such that for any n > 1, a(n) is a multiple or a divisor of a(floor(n/2)).

1, 2, 3, 4, 6, 9, 12, 8, 16, 18, 24, 27, 36, 48, 60, 32, 40, 64, 80, 54, 72, 96, 120, 81, 108, 144, 180, 192, 240, 5, 10, 128, 160, 20, 200, 256, 320, 400, 480, 162, 216, 288, 360, 384, 576, 15, 30, 243, 324, 432, 540, 720, 864, 45, 90, 768, 960, 1200, 1440

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OFFSET

1,2

COMMENTS

This sequence can be seen as an infinite complete binary tree where each node (except the root node) is a multiple or a divisor of its parent.

Will every integer appear in the sequence?

If we have a multiple of a prime number p, then the sequence contains p, and a multiple of q for any prime number q < p.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10001

Rémy Sigrist, PARI program

EXAMPLE

The first terms (arranged as a binary tree) are: