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A001692
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Number of irreducible polynomials of degree n over GF(5); dimensions of free Lie algebras.
(Formerly M3804 N1554)
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65
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1, 5, 10, 40, 150, 624, 2580, 11160, 48750, 217000, 976248, 4438920, 20343700, 93900240, 435959820, 2034504992, 9536718750, 44878791360, 211927516500, 1003867701480, 4768371093720, 22706531339280
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Exponents in expansion of Hardy-Littlewood constant C_5 = 0.409874885.. as a product_{n>=2} zeta(n)^(-a(n)).
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REFERENCES
| E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, NY, 1968, p. 84.
E. N. Gilbert and J. Riordan, Symmetry types of periodic sequences, Illinois J. Math., 5 (1961), 657-665.
M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA, 1983, p. 79.
G. J. Simmons, The number of irreducible polynomials of degree n over GF(p), Amer. Math. Monthly, 77 (1970), 743-745.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
G. Viennot, Algebres de Lie Libres et Monoides Libres, Lecture Notes in Mathematics 691, Springer verlag 1978.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..200
G. Niklasch, Some number theoretical constants: 1000-digit values [Cached copy]
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
Index entries for sequences related to Lyndon words
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FORMULA
| Sum mu(d)*5^(n/d)/n; d|n.
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PROG
| (PARI) a(n)=if(n, sumdiv(n, d, moebius(d)*5^(n/d))/n, 1) \\ Charles R Greathouse IV, Jun 15 2011
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CROSSREFS
| Cf. A001037, A054720, A002105.
5-th column of A074650. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 08 2008]
Sequence in context: A179306 A117865 A163305 * A038070 A136138 A186031
Adjacent sequences: A001689 A001690 A001691 * A001693 A001694 A001695
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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