A300675 Number of monic irreducible polynomials of degree n over GF(16) that have a given nonzero trace.

1, 8, 85, 1024, 13107, 174760, 2396745, 33554432, 477218560, 6871947672, 99955602525, 1466015503360, 21651921285435, 321685687669320, 4803839602524143, 72057594037927936, 1085102592571150095, 16397105843297320960, 248545604361560274405, 3777893186295716170752, 57567896172125197996605

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..500

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/(16*n)) * Sum_{odd d divides n} mu(d)*16^(n/d), where mu is the Möbius function A008683.

Mathematica

a[n_] := DivisorSum[n, MoebiusMu[#] * 16^(n/#) &, OddQ[#] &] / (16*n); Array[a, 21] (* Amiram Eldar, Oct 04 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, if (d%2, moebius(d)*16^(n/d)))/(16*n); \\ Michel Marcus, Mar 11 2018

Crossrefs

Column 16 of A110540.

Cf. A000048, A008683, A054660, A300674.

Sequence in context: A299176 A093103 A288691 * A241323 A349334 A261501

Adjacent sequences: A300672 A300673 A300674 * A300676 A300677 A300678

Keyword

nonn

Author

Seiichi Manyama, Mar 11 2018

Status

approved