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

%I #22 Aug 24 2023 02:31:36

%S 3,6,14,32,80,196,508,1318,3502,9382,25486,69706,192346,533830,

%T 1490406,4180416,11776896,33299124,94470780,268807044,766918996,

%U 2193322744,6286504432,18054379372,51945923740,149709932740,432139468492,1249167599632,3615732336352

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

%H Alois P. Heinz, <a href="/A114945/b114945.txt">Table of n, a(n) for n = 1..650</a>

%F a(n) ~ 3^(n+1) / (2*n). - _Vaclav Kotesovec_, Sep 05 2014

%p with(numtheory):

%p b:= n-> add(mobius(d) *3^(n/d)/n, d=divisors(n)):

%p a:= n-> add(b(k), k=1..n):

%p seq(a(n), n=1..30); # _Alois P. Heinz_, Sep 23 2008

%t f[n_] := DivisorSum[n, MoebiusMu[#] * 3^(n/#) &] / n; Accumulate[Array[f, 30]] (* _Amiram Eldar_, Aug 24 2023 *)

%o (PARI) a(n)=sum(m=1,n, 1/m* sumdiv(m, d, moebius(d)*3^(m/d) ) );/* _Joerg Arndt_, Jul 04 2011 */

%Y Partial sums of A027376. 3rd column of A143328. - _Alois P. Heinz_, Sep 23 2008

%K nonn

%O 1,1

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

%E More terms from _Alois P. Heinz_, Sep 23 2008