A338444 Lexicographically earliest sequence of distinct squarefree numbers such that for any prime p, any run of consecutive multiples of p has length exactly 2.

1, 2, 6, 3, 5, 10, 14, 7, 11, 22, 26, 13, 15, 30, 34, 17, 19, 38, 42, 21, 23, 46, 58, 29, 31, 62, 66, 33, 35, 70, 74, 37, 39, 78, 82, 41, 43, 86, 94, 47, 51, 102, 106, 53, 55, 110, 114, 57, 59, 118, 122, 61, 65, 130, 134, 67, 69, 138, 142, 71, 73, 146, 154, 77

Offset: 1

Author

Rémy Sigrist, Oct 28 2020

Keywords

• nonn

Comments

This sequence is a squarefree variant of A280864.

Conjecture: this sequence is a permutation of the squarefree numbers (A005117).

Examples

			The first terms, alongside their prime factors, are:
  n   a(n)  Prime factors
  --  ----  -------------
   1     1
   2     2  2
   3     6  2 3
   4     3    3
   5     5      5
   6    10  2   5
   7    14  2     7
   8     7        7
   9    11          11
  10    22  2       11
  11    26  2         13
  12    13            13
  13    15    3 5
  14    30  2 3 5
  15    34  2           17
  16    17              17
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, C program for A338444

Crossrefs

Cf. A005117, A280864, A338441.

Programs

C

// See Links section.