Search: id:A001692
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%I A001692 M3804 N1554
%S A001692 1,5,10,40,150,624,2580,11160,48750,217000,976248,4438920,
%T A001692 20343700,93900240,435959820,2034504992,9536718750,44878791360,
%U A001692 211927516500,1003867701480,4768371093720,22706531339280
%N A001692 Number of irreducible polynomials of degree n over GF(5); dimensions 
               of free Lie algebras.
%C A001692 Apart from initial terms, exponents in expansion of Hardy-Littlewood 
               constant C_5 as a product zeta(n)^(-a(n)).
%D A001692 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001692 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001692 E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, NY, 1968, p. 84.
%D A001692 E. N. Gilbert and J. Riordan, Symmetry types of periodic sequences, Illinois 
               J. Math., 5 (1961), 657-665.
%D A001692 M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA, 1983, 
               p. 79.
%D A001692 G. J. Simmons, The number of irreducible polynomials of degree n over 
               GF(p), Amer. Math. Monthly, 77 (1970), 743-745.
%D A001692 G. Viennot, Algebres de Lie Libres et Monoides Libres, Lecture Notes 
               in Mathematics 691, Springer verlag 1978.
%H A001692 T. D. Noe, <a href="b001692.txt">Table of n, a(n) for n=0..200</a>
%H A001692 G. Niklasch, <a href="http://www.gn-50uma.de/alula/essays/Moree/Moree.en.shtml">
               Some number theoretical constants: 1000-digit values</a>
%H A001692 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 A001692 <a href="Sindx_Lu.html#Lyndon">Index entries for sequences related to 
               Lyndon words</a>
%F A001692 Sum mu(d)*5^(n/d)/n; d|n.
%Y A001692 Cf. A001037, A054720, A002105.
%Y A001692 5-th column of A074650. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Aug 08 2008]
%Y A001692 Sequence in context: A032772 A117865 A163305 this_sequence A038070 A136138 
               A122173
%Y A001692 Adjacent sequences: A001689 A001690 A001691 this_sequence A001693 A001694 
               A001695
%K A001692 nonn,nice,easy
%O A001692 0,2
%A A001692 N. J. A. Sloane (njas(AT)research.att.com).

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