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Search: id:A001692
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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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+0
11
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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; listen)
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OFFSET
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0,2
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COMMENT
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Apart from initial terms, exponents in expansion of Hardy-Littlewood constant C_5 as a product zeta(n)^(-a(n)).
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REFERENCES
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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.
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LINKS
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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
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FORMULA
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Sum mu(d)*5^(n/d)/n; d|n.
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CROSSREFS
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Cf. A001037, A054720, A002105.
5-th column of A074650. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 08 2008]
Adjacent sequences: A001689 A001690 A001691 this_sequence A001693 A001694 A001695
Sequence in context: A121158 A032772 A117865 this_sequence A038070 A136138 A122173
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KEYWORD
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nonn,nice,easy
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AUTHOR
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njas
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