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%I #21 Oct 04 2023 05:17:21
%S 1,8,85,1024,13107,174760,2396745,33554432,477218560,6871947672,
%T 99955602525,1466015503360,21651921285435,321685687669320,
%U 4803839602524143,72057594037927936,1085102592571150095,16397105843297320960,248545604361560274405,3777893186295716170752,57567896172125197996605
%N Number of monic irreducible polynomials of degree n over GF(16) that have a given nonzero trace.
%H Seiichi Manyama, <a href="/A300675/b300675.txt">Table of n, a(n) for n = 1..500</a>
%H F. Ruskey, C.R. Miers, and J. Sawada, <a href="https://doi.org/10.1137/S0895480100368050">The number of irreducible polynomials and Lyndon words with given trace</a>, SIAM J. Discrete Math. 14 (2001), 240-245.
%F a(n) = (1/(16*n)) * Sum_{odd d divides n} mu(d)*16^(n/d), where mu is the Möbius function A008683.
%t a[n_] := DivisorSum[n, MoebiusMu[#] * 16^(n/#) &, OddQ[#] &] / (16*n); Array[a, 21] (* _Amiram Eldar_, Oct 04 2023 *)
%o (PARI) a(n) = sumdiv(n, d, if (d%2, moebius(d)*16^(n/d)))/(16*n); \\ _Michel Marcus_, Mar 11 2018
%Y Cf. A000048, A008683, A054660, A300674.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Mar 11 2018
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