%I A001371 M0115 N0045
%S A001371 1,2,1,2,3,6,8,16,24,42,69,124,208,378,668,1214,2220,4110,7630,
%T A001371 14308,26931,50944,96782,184408,352450,675180,1296477,2493680,
%U A001371 4805388,9272778,17919558,34669600,67156800,130215996,252741255
%N A001371 Number of n-bead necklaces with beads of 2 colors and primitive period 
               n, when turning over is allowed.
%D A001371 E. N. Gilbert and J. Riordan, Symmetry types of periodic sequences, Illinois 
               J. Math., 5 (1961), 657-665.
%D A001371 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001371 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A001371 F. Ruskey, <a href="http://www.theory.cs.uvic.ca/~cos/inf/neck/NecklaceInfo.html">
               Necklaces, Lyndon words, De Bruijn sequences, etc.</a>
%H A001371 <a href="Sindx_Ne.html#necklaces">Index entries for sequences related 
               to necklaces</a>
%F A001371 Sum_{ d divides n } mu(d)*A000029(n/d).
%p A001371 with(numtheory); A001371 := proc(n) local s,d; if n = 0 then RETURN(1) 
               else s := 0; for d in divisors(n) do s := s+mobius(d)*A000029(n/d); 
               od; RETURN(s); fi; end;
%Y A001371 Sequence in context: A108618 A097719 A056493 this_sequence A001037 A122086 
               A082594
%Y A001371 Adjacent sequences: A001368 A001369 A001370 this_sequence A001372 A001373 
               A001374
%K A001371 nonn,easy,nice
%O A001371 0,2
%A A001371 N. J. A. Sloane (njas(AT)research.att.com).
%E A001371 More terms from Christian G. Bower (bowerc(AT)usa.net)