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

1,2

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).

Sequence in context: A026508 A184103 A352318 * A285302 A026281 A066994

Adjacent sequences: A284035 A284036 A284037 * A284039 A284040 A284041

Keyword

nonn

Author

Rémy Sigrist, May 25 2017

Status

approved