cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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).

Original entry on oeis.org

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

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Author

Rémy Sigrist, Sep 28 2024

Keywords

Comments

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

Examples

			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
		

Crossrefs

Cf. A025523.

Programs

  • 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;););); }

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