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A192509
Number of conjugacy classes of primitive elements in GF(7^n) which have trace 0.
6
0, 0, 3, 20, 160, 846, 5426, 27360, 196740, 1215548, 8552408, 37330020
OFFSET
1,3
COMMENTS
Also number of primitive polynomials of degree n over GF(7) whose second-highest coefficient is 0.
FORMULA
a(n) = A192214(n) / n.
PROG
(GAP)
p := 7;
a := function(n)
local q, k, cnt, x;
q:=p^n; k:=GF(p, n); cnt:=0;
for x in k do
if Trace(k, GF(p), x)=0*Z(p) and Order(x)=q-1 then
cnt := cnt+1;
fi;
od;
return cnt/n;
end;
for n in [1..16] do Print (a(n), ", "); od;
(Sage) # See A192507 (change first line p=3 to p=7)
CROSSREFS
Cf. A152049 (GF(2^n)), A192507 (GF(3^n)), A192508 (GF(5^n)), A192510 (GF(11^n)), A192511 (GF(13^n)).
Sequence in context: A123355 A371815 A258791 * A336653 A012882 A063017
KEYWORD
nonn,hard,more
AUTHOR
Joerg Arndt, Jul 03 2011
EXTENSIONS
a(7)-a(9) from Joerg Arndt, Oct 14 2012
a(10)-a(12) from Robin Visser, Jun 01 2024
STATUS
approved