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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
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OFFSET
1,3
LINKS
Table of n, a(n) for n=1..21.
FORMULA
a(n) = n *
A192507
(n). [
Joerg Arndt
, Oct 03 2012]
PROG
(SageMath)
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
Adjacent sequences:
A192209
A192210
A192211
*
A192213
A192214
A192215
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
