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A192510 Number of conjugacy classes of primitive elements in GF(11^n) which have trace 0.

%I A192510 #17 May 10 2024 08:52:24
%S A192510 0,0,16,80,1185,5656,98840,638400,7734524,62848400
%N A192510 Number of conjugacy classes of primitive elements in GF(11^n) which have trace 0.
%C A192510 Also number of primitive polynomials of degree n over GF(11) whose second-highest coefficient is 0.
%F A192510 a(n) = A192215(n) / n.
%o A192510 (GAP)
%o A192510 p := 11;
%o A192510 a := function(n)
%o A192510     local q, k, cnt, x;
%o A192510     q:=p^n;  k:=GF(p, n);  cnt:=0;
%o A192510     for x in k do
%o A192510         if Trace(k, GF(p), x)=0*Z(p) and Order(x)=q-1 then
%o A192510             cnt := cnt+1;
%o A192510         fi;
%o A192510     od;
%o A192510     return cnt/n;
%o A192510 end;
%o A192510 for n in [1..16] do  Print (a(n), ", ");  od;
%o A192510 (Sage) # See A192507 (change first line p=3 to p=11)
%Y A192510 Cf. A152049 (GF(2^n)), A192507 (GF(3^n)), A192508 (GF(5^n)), A192509 (GF(7^n)), A192511 (GF(13^n)).
%K A192510 nonn,hard,more
%O A192510 1,3
%A A192510 _Joerg Arndt_, Jul 03 2011
%E A192510 Added terms a(6) and a(7), _Joerg Arndt_, Oct 14 2012
%E A192510 a(8)-a(10) from _Robin Visser_, May 10 2024