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

Author

Jay Anderson, Sep 07 2023

Keywords

• nonn

Examples

			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}).
		

Crossrefs

Cf. A008683, A015134.

Programs

Mathematica

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

Formula

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

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