A115123 - OEIS

%I #6 Aug 28 2019 08:15:47

%S 0,1,1,2,1,5,1,9,4,22,1,63,1,156,24,469,1,1532,1,4889,158,16546,1,

%T 57844,21,202061,1480,720533,1,2598406,1,9408469,16548,34350508,175,

%U 126167112,1,465200334,202063,1723346534,1,6409076632,1,23911272097,2594970,89495909410,1

%N Number of imprimitive (periodic) bracelets (or necklaces) with n red and blue beads such that the beads switch colors when bracelet is turned over.

%C a(p)=1 for prime p.

%F a(n)=A006080(n+1) - A066315(n).

%t A006080[n_] := Sum[EulerPhi[(n - 1)/k] (Binomial[2k, k]/(2(n - 1))), {k, Divisors[n - 1]}]/2 + 2^(n - 3); A006080[1] = 1;

%t A066315[n_] := Sum[MoebiusMu[n/d] A006080[d + 1], {d, Divisors[n]}];

%t a[n_] := A006080[n + 1] - A066315[n];

%t Array[a, 60] (* _Jean-François Alcover_, Aug 28 2019 *)

%K easy,nonn

%O 1,4

%A _Valery A. Liskovets_, Jan 17 2006

%E More terms from _Jean-François Alcover_, Aug 28 2019