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Number of imprimitive (periodic) bracelets (or necklaces) with n red or blue beads such that the beads switch colors when bracelet is turned over.
2

%I #11 Aug 28 2019 04:47:00

%S 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 625,1,1160,1,2122,95,3857,13,7612,1,13799,317,26518,1,50559,1,95887,

%U 1124,182363,1,352750,10,671150,3857,1292764,1,2492933,97,4797904,13799

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

%C Presumably a(n) = A115118(n) = A066656(n)/2 for odd n.

%F a(n) = A053656(n) - A066313(n).

%t A053656[n_] := Total[EulerPhi[#] 2^(n/#)& /@ Divisors[n]]/(2n) + 2^(n/2-2)* (1 - Mod[n, 2]);

%t A066313[n_] := DivisorSum[n, A053656[#] MoebiusMu[n/#]&];

%t a[n_] := A053656[n] - A066313[n];

%t Array[a, 35] (* _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