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

Author

Rémy Sigrist, Jan 06 2020

Keywords

• nonn
• look
• tabf

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.

Examples

			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]
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers
• Rémy Sigrist, PARI program for A331010

Crossrefs

See A331016, A331018 and A331026 for similar sequences.

Cf. A000005, A027750.

Programs

PARI

See Links section.