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A192508
Number of conjugacy classes of primitive elements in GF(5^n) which have trace 0.
5
0, 0, 4, 8, 54, 140, 1116, 2976, 19828, 58388, 443892, 1036180, 9390024, 27996724, 175396812
OFFSET
1,3
COMMENTS
Also number of primitive polynomials of degree n over GF(5) whose second-highest coefficient is 0.
FORMULA
a(n) = A192213(n) / n
PROG
(GAP)
p := 5;
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=5)
CROSSREFS
Cf. A152049 (GF(2^n)), A192507 (GF(3^n)), A192509 (GF(7^n)), A192510 (GF(11^n)), A192511 (GF(13^n)).
Sequence in context: A215746 A128893 A214603 * A231601 A347511 A123106
KEYWORD
nonn,hard,more
AUTHOR
Joerg Arndt, Jul 03 2011
EXTENSIONS
Added terms 19828..443892, Joerg Arndt, Oct 03 2012
a(12)-a(15) from Robin Visser, May 10 2024
STATUS
approved