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A300674 Number of monic irreducible polynomials of degree n over GF(8) that have a given nonzero trace. 2
1, 4, 21, 128, 819, 5460, 37449, 262144, 1864128, 13421772, 97612893, 715827840, 5286113595, 39268272420, 293203100463, 2199023255552, 16557351571215, 125099989647360, 948126237341157, 7205759403792768, 54901024028884989, 419244183493398900, 3208129404123400281, 24595658764945981440 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..1000

F. Ruskey, C.R. Miers, J. Sawada, The number of irreducible polynomials and Lyndon words with given trace, SIAM J. Discrete Math. 14 (2001) 240-245.

FORMULA

a(n) = (1/(8*n)) * Sum_{odd d divides n} mu(d)*8^(n/d), where mu is the Möbius function A008683.

PROG

(PARI) a(n) = sumdiv(n, d, if (d%2, moebius(d)*8^(n/d)))/(8*n); \\ Michel Marcus, Mar 11 2018

CROSSREFS

Cf. A000048, A054660, A300675.

Sequence in context: A255673 A099250 A293192 * A232956 A234268 A111177

Adjacent sequences:  A300671 A300672 A300673 * A300675 A300676 A300677

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Mar 11 2018

STATUS

approved

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Last modified April 3 23:48 EDT 2020. Contains 333207 sequences. (Running on oeis4.)