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

Author

Seiichi Manyama, Mar 11 2018

Keywords

• nonn

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.

Crossrefs

Column 8 of A110540.

Cf. A000048, A008683, A054660, A300675.

Programs

Mathematica

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

PARI

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

Formula

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