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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

LINKS

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

Rémy Sigrist, PARI program for A334766

FORMULA

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

EXAMPLE

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

PROG

(PARI) See Links section.

CROSSREFS

Cf. A106490, A182318, A298480.

Sequence in context: A075554 A294103 A137369 * A336847 A294063 A290096

Adjacent sequences:  A334763 A334764 A334765 * A334767 A334768 A334769

KEYWORD

nonn

AUTHOR

Rémy Sigrist, May 10 2020

STATUS

approved

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Last modified September 29 21:59 EDT 2020. Contains 337432 sequences. (Running on oeis4.)