Search: id:A001693
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%I A001693 M4373 N1838
%S A001693 1,7,21,112,588,3360,19544,117648,720300,4483696,28245840,
%T A001693 179756976,1153430600,7453000800,48444446376,316504099520,
%U A001693 2077057800300,13684147881600,90467419857752,599941851861744
%N A001693 Number of degree-n irreducible polynomials over GF(7); dimensions of 
               free Lie algebras.
%D A001693 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001693 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001693 E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, NY, 1968, p. 84.
%D A001693 M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA, 1983, 
               p. 79.
%D A001693 G. J. Simmons, The number of irreducible polynomials of degree n over 
               GF(p), Amer. Math. Monthly, 77 (1970), 743-745.
%D A001693 G. Viennot, Algebres de Lie Libres et Monoides Libres, Lecture Notes 
               in Mathematics 691, Springer verlag 1978.
%H A001693 T. D. Noe, <a href="b001693.txt">Table of n, a(n) for n=0..200</a>
%H A001693 Y. Puri and T. Ward, <a href="http://www.cs.uwaterloo.ca/journals/JIS/
               index.html">Arithmetic and growth of periodic orbits</a>, J. Integer 
               Seqs., Vol. 4 (2001), #01.2.1.
%H A001693 <a href="Sindx_Lu.html#Lyndon">Index entries for sequences related to 
               Lyndon words</a>
%F A001693 a(n) = (1/n)*Sum_{d|n} mu(d)*7^(n/d).
%p A001693 with(numtheory); A001693 := proc(n) local d,s; if n = 0 then RETURN(1); 
               else s := 0; for d in divisors(n) do s := s+mobius(d)*7^(n/d); od; 
               RETURN(s/n); fi; end;
%Y A001693 Cf. A027376, A000031, A001037.
%Y A001693 Sequence in context: A121157 A038184 A001185 this_sequence A061961 A028248 
               A032032
%Y A001693 Adjacent sequences: A001690 A001691 A001692 this_sequence A001694 A001695 
               A001696
%K A001693 nonn,easy,nice
%O A001693 0,2
%A A001693 N. J. A. Sloane (njas(AT)research.att.com).
%E A001693 Description corrected by Vladeta Jovovic (vladeta(AT)EUnet.yu), Feb 09, 
               2001.

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