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A001692 Number of irreducible polynomials of degree n over GF(5); dimensions of free Lie algebras.
(Formerly M3804 N1554)
+0
11
1, 5, 10, 40, 150, 624, 2580, 11160, 48750, 217000, 976248, 4438920, 20343700, 93900240, 435959820, 2034504992, 9536718750, 44878791360, 211927516500, 1003867701480, 4768371093720, 22706531339280 (list; graph; listen)
OFFSET

0,2

COMMENT

Apart from initial terms, exponents in expansion of Hardy-Littlewood constant C_5 as a product zeta(n)^(-a(n)).

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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.

G. Viennot, Algebres de Lie Libres et Monoides Libres, Lecture Notes in Mathematics 691, Springer verlag 1978.

LINKS

T. D. Noe, Table of n, a(n) for n=0..200

G. Niklasch, Some number theoretical constants: 1000-digit values

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

FORMULA

Sum mu(d)*5^(n/d)/n; d|n.

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: A032772 A117865 A163305 this_sequence A038070 A136138 A122173

Adjacent sequences: A001689 A001690 A001691 this_sequence A001693 A001694 A001695

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

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Last modified December 1 19:22 EST 2009. Contains 167811 sequences.


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