A365519 Moebius inversion of A015134.

1, 1, 1, 2, 2, 1, 3, 4, 3, 2, 13, 4, 6, 3, 8, 8, 8, 9, 21, 8, 24, 13, 11, 16, 10, 6, 9, 12, 62, 8, 33, 16, 24, 24, 24, 36, 18, 63, 24, 32, 42, 24, 21, 48, 24, 33, 69, 64, 21, 10, 32, 24, 26, 27, 144, 48, 40, 62, 61, 32, 62, 99, 72, 32, 48, 24, 33, 96, 88, 24

Offset

1,4

Links

Table of n, a(n) for n=1..70.

Formula

a(n) = Sum_{d|n} moebius(d)*A015134(n/d).

A015134(n) = Sum_{d|n} a(d).

Example

For n=4, the a(4) = 2 cycles counted are
  {0 1 1 2 3 1} repeating
  {0 3 3 2 1 3} repeating
There are 2 other cycles {0} and {0 2 2} mod 4 which are not counted because they are multiples of cycles counted at earlier n (n=1 for {0} and n=2 for {0 1 1}*2 = {0 2 2}).

Mathematica

a[n_]:=Sum[MoebiusMu[d]Part[ResourceFunction["OEISSequence"]["A015134"], n/d], {d, Divisors[n]}]; Array[a, 70] (* Stefano Spezia, Sep 27 2023 *)

Crossrefs

Cf. A008683, A015134.

Sequence in context: A091594 A118032 A089692 * A349346 A066201 A303273

Adjacent sequences: A365516 A365517 A365518 * A365520 A365521 A365522

Keyword

nonn

Author

Jay Anderson, Sep 07 2023

Status

approved