%I #18 Apr 26 2024 12:36:36

%S 0,0,3,8,35,84,364,832,2997,8700,28281,55080,265720,794304,2006730,

%T 5240928,21511647,47028492,193587884,415388400,1607804226

%N Number of zero trace primitive elements in Galois field GF(3^n)

%F a(n) = n * A192507(n). [_Joerg Arndt_, Oct 03 2012]

%o (Sage)

%o def a(n):

%o ans = 0

%o for x in GF(3^n):

%o if x!=0 and x.trace()==0 and x.multiplicative_order()==3^n-1: ans += 1

%o return ans # _Robin Visser_, Apr 26 2024

%Y Cf. A192211, A192213, A192214, A192215, A192216 for other primes

%K nonn,hard,more

%O 1,3

%A _Pasha Zusmanovich_, Jun 25 2011

%E a(12)-a(17) from _Joerg Arndt_, Oct 03 2012

%E a(18)-a(21) from _Robin Visser_, Apr 26 2024