A331010 Lexicographically earliest sequence of distinct positive terms that can be viewed as an irregular table where the n-th row has A000005(a(n)) terms and T(n, k) is a multiple of the k-th divisor of a(n) (=A027750(a(n), k)).

1, 2, 4, 3, 6, 8, 5, 9, 7, 10, 12, 18, 11, 14, 16, 24, 13, 15, 17, 21, 27, 19, 28, 20, 22, 25, 30, 23, 26, 33, 32, 36, 48, 29, 34, 39, 42, 45, 54, 31, 44, 35, 38, 49, 56, 37, 40, 52, 64, 80, 41, 46, 51, 60, 66, 72, 84, 96, 43, 65, 47, 57, 50, 75, 53, 68, 55

Offset

1,2

Comments

This sequence is a permutation of the natural numbers as each row starts with the least value not yet in the sequence.

The prime numbers appear in ascending order.

Links

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

Rémy Sigrist, PARI program for A331010.

Index entries for sequences that are permutations of the natural numbers.

Example

The first terms and rows are:
  n   a(n)  row(n)
  --  ----  -------------------------
   1     1  [1]
   2     2  [2, 4]
   3     4  [3, 6, 8]
   4     3  [5, 9]
   5     6  [7, 10, 12, 18]
   6     8  [11, 14, 16, 24]
   7     5  [13, 15]
   8     9  [17, 21, 27]
   9     7  [19, 28]
  10    10  [20, 22, 25, 30]
  11    12  [23, 26, 33, 32, 36, 48]
  12    18  [29, 34, 39, 42, 45, 54]
  13    11  [31, 44]
  14    14  [35, 38, 49, 56]
  15    16  [37, 40, 52, 64, 80]
  16    24  [41, 46, 51, 60, 66, 72, 84, 96]

Prog

(PARI) \\ See Links section.

Crossrefs

See A331016, A331018 and A331026 for similar sequences.

Cf. A000005, A027750.

Sequence in context: A178898 A296616 A143529 * A261351 A249054 A103867

Adjacent sequences: A331007 A331008 A331009 * A331011 A331012 A331013

Keyword

nonn,look,tabf

Author

Rémy Sigrist, Jan 06 2020

Status

approved