A300674 Number of monic irreducible polynomials of degree n over GF(8) that have a given nonzero trace.

1, 4, 21, 128, 819, 5460, 37449, 262144, 1864128, 13421772, 97612893, 715827840, 5286113595, 39268272420, 293203100463, 2199023255552, 16557351571215, 125099989647360, 948126237341157, 7205759403792768, 54901024028884989, 419244183493398900, 3208129404123400281, 24595658764945981440

Offset

1,2

Links

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

F. Ruskey, C.R. Miers, and 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.

Mathematica

a[n_] := DivisorSum[n, MoebiusMu[#] * 8^(n/#) &, OddQ[#] &] / (8*n); Array[a, 24] (* Amiram Eldar, Oct 04 2023 *)

Prog

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

Crossrefs

Column 8 of A110540.

Cf. A000048, A008683, A054660, A300675.

Sequence in context: A255673 A099250 A293192 * A371430 A232956 A234268

Adjacent sequences: A300671 A300672 A300673 * A300675 A300676 A300677

Keyword

nonn

Author

Seiichi Manyama, Mar 11 2018

Status

approved