%I #35 Jan 20 2024 03:54:47

%S 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,

%T 33,16,24,24,24,36,18,63,24,32,42,24,21,48,24,33,69,64,21,10,32,24,26,

%U 27,144,48,40,62,61,32,62,99,72,32,48,24,33,96,88,24

%N Moebius inversion of A015134.

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

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

%e For n=4, the a(4) = 2 cycles counted are

%e {0 1 1 2 3 1} repeating

%e {0 3 3 2 1 3} repeating

%e 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}).

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

%Y Cf. A008683, A015134.

%K nonn

%O 1,4

%A _Jay Anderson_, Sep 07 2023