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).

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, 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, 1, 5, 1, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1

Offset

1,2

Comments

The sequence is well defined as we can always extend it with a number greater than any prior term.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Formula

a(2*k-1) = 1 for any k > 0.

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

Example

The first terms, alongside the corresponding k's, are:
  n   a(n)  k's
  --  ----  ---------------------------------------------
   1     1  None
   2     2  None
   3     1  1, 2
   4     3  None
   5     1  1, 2, 3, 4
   6     4  None
   7     1  1, 2, 3, 4, 5, 6
   8     2  2, 6
   9     1  1, 2, 3, 4, 5, 6, 7, 8
  10     5  None
  11     1  1, 2, 3, 4, 5, 6, 7, 8, 9, 10
  12     6  None
  13     1  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
  14     2  2, 6, 8, 12
  15     1  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
  16     3  4, 12

Prog

(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; ); ); ); }

Crossrefs

Cf. A025523.

Sequence in context: A289508 A364448 A028920 * A260738 A055396 A363486

Adjacent sequences: A376563 A376564 A376565 * A376567 A376568 A376569

Keyword

nonn

Author

Rémy Sigrist, Sep 28 2024

Status

approved