A284038 Lexicographically earliest sequence of distinct positive terms such that A000196(n) divides a(n).

1, 2, 3, 4, 6, 8, 10, 12, 9, 15, 18, 21, 24, 27, 30, 16, 20, 28, 32, 36, 40, 44, 48, 52, 5, 25, 35, 45, 50, 55, 60, 65, 70, 75, 80, 42, 54, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 7, 14, 49, 56, 63, 77, 91, 98, 105, 112, 119, 133, 140, 147, 154, 64

Offset: 1

Author

Rémy Sigrist, May 25 2017

Keywords

• nonn

Comments

This is a permutation of the natural numbers, with inverse A287433; for any n > 0, n appears among the first n^2 terms.

This sequence is similar to A075383: here we have runs of length 2*k+1, there of length k, of multiples of k.

a(p^2) = p for any prime p > 3.

All fixed points belong to A006446.

Conjecturally:

- all fixed points > 3 are squares,

- if a(n) < n, then A000196(n) belongs to A007310 \ {1},

- if k belongs to A007310 \ {1}, then a(n) < n for some n such that A000196(n) = k.

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A284038
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000196, A006446, A007310, A075383, A287433 (inverse).