A334766 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, the prime tower factorization of a(n+1) can be obtained from that of a(n) by adding or removing exactly one prime number.

1, 2, 4, 12, 6, 3, 9, 18, 36, 144, 48, 16, 80, 20, 10, 5, 15, 30, 60, 180, 90, 45, 225, 75, 25, 50, 100, 300, 150, 450, 900, 3600, 720, 240, 1200, 400, 2800, 560, 112, 28, 14, 7, 21, 42, 84, 252, 126, 63, 315, 105, 35, 70, 140, 420, 210, 630, 1260, 5040, 1008

Offset: 1

Author

Rémy Sigrist, May 10 2020

Keywords

• nonn

Comments

The prime tower factorization of a number is defined in A182318.

For any n > 0, a(n+1) is either a multiple or a divisor of a(n).

For any prime number p, the sequence contains a multiple of p.

Examples

			The first terms, alongside their prime tower factorizations, are:
  n   a(n)  Prime tower factorization of a(n)
  --  ----  ---------------------------------
   1     1  1
   2     2  2
   3     4  2^2
   4    12  2^2   * 3
   5     6  2     * 3
   6     3          3
   7     9          3^2
   8    18  2     * 3^2
   9    36  2^2   * 3^2
  10   144  2^2^2 * 3^2
  11    48  2^2^2 * 3
  12    16  2^2^2
  13    80  2^2^2       * 5
  14    20  2^2         * 5
  15    10  2           * 5
  16     5                5
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A334766

Crossrefs

Cf. A106490, A182318, A298480.

Programs

PARI

See Links section.

Formula

abs(A106490(a(n+1)) - A106490(a(n))) = 1.