A114945 Number of monic irreducible polynomials over GF(3) of degree <= n.

3, 6, 14, 32, 80, 196, 508, 1318, 3502, 9382, 25486, 69706, 192346, 533830, 1490406, 4180416, 11776896, 33299124, 94470780, 268807044, 766918996, 2193322744, 6286504432, 18054379372, 51945923740, 149709932740, 432139468492, 1249167599632, 3615732336352

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..650

Crossrefs

Partial sums of A027376. 3rd column of A143328. - Alois P. Heinz, Sep 23 2008

Programs

Maple

with(numtheory):
b:= n-> add(mobius(d) *3^(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[#] * 3^(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)*3^(m/d) ) );/* Joerg Arndt, Jul 04 2011 */

Formula

a(n) ~ 3^(n+1) / (2*n). - Vaclav Kotesovec, Sep 05 2014

Extensions

More terms from Alois P. Heinz, Sep 23 2008