A054662 Number of monic irreducible polynomials over GF(5) with fixed nonzero trace.

1, 2, 8, 30, 125, 516, 2232, 9750, 43400, 195250, 887784, 4068740, 18780048, 87191964, 406901000, 1907343750, 8975758272, 42385503300, 200773540296, 953674218750, 4541306267856, 21674415838068, 103660251783288

Offset: 1

Author

N. J. A. Sloane, Apr 18 2000

Keywords

• nonn
• easy

Comments

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).

Links

• Frank Ruskey, Number of monic irreducible polynomials over GF(q) with given trace
• Frank Ruskey, Number of q-ary Lyndon words with given trace mod q
• Frank Ruskey, Number of Lyndon words over GF(q) with given trace

Crossrefs

Column 5 of A110540.

Cf. A000048, A051841, A046211, A046209, A054661, etc.

Programs

PARI

a(n) = sumdiv(n, d, (gcd(d, 5)==1)*(moebius(d)*5^(n/d)))/(5*n); \\ Seiichi Manyama, May 29 2024

Formula

a(n) = 1/(5*n) * Sum_{d|n, gcd(d,5)=1} mu(d) * 5^(n/d). - Seiichi Manyama, May 29 2024

Extensions

More terms from James Sellers, Apr 19 2000