login
A192212
Number of zero trace primitive elements in Galois field GF(3^n)
6
0, 0, 3, 8, 35, 84, 364, 832, 2997, 8700, 28281, 55080, 265720, 794304, 2006730, 5240928, 21511647, 47028492, 193587884, 415388400, 1607804226
OFFSET
1,3
FORMULA
a(n) = n * A192507(n). [Joerg Arndt, Oct 03 2012]
PROG
(Sage)
def a(n):
ans = 0
for x in GF(3^n):
if x!=0 and x.trace()==0 and x.multiplicative_order()==3^n-1: ans += 1
return ans # Robin Visser, Apr 26 2024
CROSSREFS
Cf. A192211, A192213, A192214, A192215, A192216 for other primes
Sequence in context: A349968 A204451 A077291 * A148918 A304726 A226679
KEYWORD
nonn,hard,more
AUTHOR
Pasha Zusmanovich, Jun 25 2011
EXTENSIONS
a(12)-a(17) from Joerg Arndt, Oct 03 2012
a(18)-a(21) from Robin Visser, Apr 26 2024
STATUS
approved