cp's OEIS Frontend

A115121 Number of imprimitive (periodic) bracelets (or necklaces) with n red or blue beads such that the beads switch colors when bracelet is turned over.

%I A115121 #11 Aug 28 2019 04:47:00
%S A115121 0,1,1,2,1,3,1,4,2,5,1,11,1,11,5,22,1,37,1,64,11,95,1,210,4,317,30,
%T A115121 625,1,1160,1,2122,95,3857,13,7612,1,13799,317,26518,1,50559,1,95887,
%U A115121 1124,182363,1,352750,10,671150,3857,1292764,1,2492933,97,4797904,13799
%N A115121 Number of imprimitive (periodic) bracelets (or necklaces) with n red or blue beads such that the beads switch colors when bracelet is turned over.
%C A115121 a(p)=1 for prime p.
%C A115121 Presumably a(n) = A115118(n) = A066656(n)/2 for odd n.
%F A115121 a(n) = A053656(n) - A066313(n).
%t A115121 A053656[n_] := Total[EulerPhi[#] 2^(n/#)& /@ Divisors[n]]/(2n) + 2^(n/2-2)* (1 - Mod[n, 2]);
%t A115121 A066313[n_] := DivisorSum[n, A053656[#] MoebiusMu[n/#]&];
%t A115121 a[n_] := A053656[n] - A066313[n];
%t A115121 Array[a, 35] (* _Jean-François Alcover_, Aug 28 2019 *)
%K A115121 easy,nonn
%O A115121 1,4
%A A115121 _Valery A. Liskovets_, Jan 17 2006
%E A115121 More terms from _Jean-François Alcover_, Aug 28 2019