A114947 Number of monic irreducible polynomials over GF(5) of degree <= n.

5, 15, 55, 205, 829, 3409, 14569, 63319, 280319, 1256567, 5695487, 26039187, 119939427, 555899247, 2590404239, 12127122989, 57005914349, 268933430849, 1272801132329, 6041172226049, 28747703565329, 137119782755669, 655421041672109, 3138947897124609

Offset: 1

Author

Gary L Mullen (mullen(AT)math.psu.edu) and Ken Hicks, Jan 06 2006

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Partial sums of A001692. 5th column of A143328. - Alois P. Heinz, Sep 23 2008

Programs

Maple

with(numtheory):
b:= n-> add(mobius(d) *5^(n/d)/n, d=divisors(n)):
a:= n-> add(b(k), k=1..n):
seq(a(n), n=1..30); # Alois P. Heinz, Sep 23 2008

Mathematica

f[n_] := DivisorSum[n, MoebiusMu[#] * 5^(n/#) &] / n; Accumulate[Array[f, 30]] (* Amiram Eldar, Aug 24 2023 *)

PARI

a(n)=sum(m=1, n, 1/m* sumdiv(m, d, moebius(d)*5^(m/d) ) ); /* Joerg Arndt, Jul 04 2011 */

Formula

a(n) ~ 5^(n+1) / (4*n). - Vaclav Kotesovec, Sep 05 2014

Extensions

More terms from Alois P. Heinz, Sep 23 2008