%I #20 May 29 2024 13:47:14
%S 1,2,8,30,125,516,2232,9750,43400,195250,887784,4068740,18780048,
%T 87191964,406901000,1907343750,8975758272,42385503300,200773540296,
%U 953674218750,4541306267856,21674415838068,103660251783288
%N Number of monic irreducible polynomials over GF(5) with fixed nonzero trace.
%C Also number of 5-ary Lyndon words with trace 1 mod 5; trace 2 mod 5; trace 3 mod 5; trace 4 mod 5; also number of 5-ary Lyndon words of trace 1 over GF(5), trace 2 over GF(5); trace 3 over GF(5); trace 4 over GF(5).
%H Frank Ruskey, <a href="http://combos.org/Tpoly">Number of monic irreducible polynomials over GF(q) with given trace</a>
%H Frank Ruskey, <a href="http://combos.org/TlyndonZk">Number of q-ary Lyndon words with given trace mod q</a>
%H Frank Ruskey, <a href="http://combos.org/TlyndonFk">Number of Lyndon words over GF(q) with given trace</a>
%F a(n) = 1/(5*n) * Sum_{d|n, gcd(d,5)=1} mu(d) * 5^(n/d). - _Seiichi Manyama_, May 29 2024
%o (PARI) a(n) = sumdiv(n, d, (gcd(d, 5)==1)*(moebius(d)*5^(n/d)))/(5*n); \\ _Seiichi Manyama_, May 29 2024
%Y Column 5 of A110540.
%Y Cf. A000048, A051841, A046211, A046209, A054661, etc.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Apr 18 2000
%E More terms from _James A. Sellers_, Apr 19 2000