A288921 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms has at least 34 divisors.

1, 1260, 2, 630, 4, 315, 8, 180, 7, 240, 6, 210, 10, 126, 16, 90, 14, 120, 12, 105, 20, 63, 32, 45, 28, 60, 21, 80, 18, 70, 24, 75, 36, 35, 48, 30, 42, 40, 54, 50, 66, 56, 72, 25, 84, 15, 96, 33, 100, 27, 112, 39, 132, 49, 108, 44, 117, 64, 81, 88, 78, 98, 99

Offset: 1

Author

Rémy Sigrist, Jun 19 2017

Keywords

• nonn
• look

Comments

The number of divisors is given by A000005.

This sequence is a permutation of the natural numbers, with inverse A288922.

Conjecturally, a(n) ~ n.

See also A288923 for similar sequences.

Examples

			The first terms, alongside a(n)*a(n+1) and its number of divisors, are:
   n    a(n)  a(n)*a(n+1)   Number of divisors
  --   ----   -----------   ------------------
   1      1       1260              36
   2   1260       2520              48
   3      2       1260              36
   4    630       2520              48
   5      4       1260              36
   6    315       2520              48
   7      8       1440              36
   8    180       1260              36
   9      7       1680              40
  10    240       1440              36
  11      6       1260              36
  12    210       2100              36
  13     10       1260              36
  14    126       2016              36
  15     16       1440              36
  16     90       1260              36
  17     14       1680              40
  18    120       1440              36
  19     12       1260              36
  20    105       2100              36
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..30000
• Rémy Sigrist, PARI program for A288921
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000005, A288922 (inverse), A288923.