Search: id:A000046
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%I A000046 M0696 N0257
%S A000046 1,1,1,1,2,3,5,8,14,21,39,62,112,189,352,607,1144,2055,3885,7154,
%T A000046 13602,25472,48670,92204,176770,337590,649341,1246840,2404872,4636389,
%U A000046 8964143,17334800,33587072,65107998,126387975,245492232,477349348
%N A000046 Number of primitive n-bead necklaces (turning over is allowed) where 
               complements are equivalent.
%D A000046 E. N. Gilbert and J. Riordan, Symmetry types of periodic sequences, Illinois 
               J. Math., 5 (1961), 657-665.
%D A000046 B. Gruenbaum and G. C. Shephard, The geometry of fabrics, pp. 77-98 of 
               F. C. Holroyd and R. J. Wilson, editors, Geometrical Combinatorics. 
               Pitman, Boston, 1984.
%D A000046 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000046 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000046 Christian G. Bower, <a href="b000046.txt">Table of n, a(n) for n = 0..1000</
               a>
%H A000046 <a href="Sindx_Ne.html#necklaces">Index entries for sequences related 
               to necklaces</a>
%F A000046 Sum_{ d divides n } mu(d)*A000011(n/d).
%p A000046 with(numtheory); A000046 := proc(n) local s,d; if n = 0 then RETURN(1); 
               else s := 0; for d in divisors(n) do s := s+mobius(d)*A000011(n/d); 
               od; RETURN(s); fi; end;
%Y A000046 Similar to A000011, but counts primitive necklaces.
%Y A000046 Cf. A054199.
%Y A000046 Sequence in context: A034413 A034416 A056366 this_sequence A131132 A004692 
               A094926
%Y A000046 Adjacent sequences: A000043 A000044 A000045 this_sequence A000047 A000048 
               A000049
%K A000046 nonn,easy,nice
%O A000046 0,5
%A A000046 N. J. A. Sloane (njas(AT)research.att.com).

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