A373277 Number of monic irreducible polynomials over GF(7) with fixed nonzero trace.

1, 3, 16, 84, 480, 2792, 16807, 102900, 640528, 4035120, 25679568, 164775800, 1064714400, 6920635197, 45214871360, 296722542900, 1954878268800, 12923917122536, 85705978837392, 569944757250960, 3799631728452112, 25388448354582216, 169992219503608176

Offset

1,2

Links

Table of n, a(n) for n=1..23.

Frank Ruskey, Number of monic irreducible polynomials over GF(q) with given trace

Formula

a(n) = 1/(7*n) * Sum_{d|n, gcd(d,7)=1} mu(d) * 7^(n/d).

Prog

(PARI) a(n) = sumdiv(n, d, (gcd(d, 7)==1)*(moebius(d)*7^(n/d)))/(7*n);

Crossrefs

Column 7 of A110540.

Sequence in context: A026131 A026160 A025187 * A151328 A277923 A076279

Adjacent sequences: A373274 A373275 A373276 * A373278 A373279 A373280

Keyword

nonn

Author

Seiichi Manyama, May 29 2024

Status

approved