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A192213
Number of zero trace primitive elements in Galois field GF(5^n).
6
0, 0, 12, 32, 270, 840, 7812, 23808, 178452, 583880, 4882812, 12434160, 122070312, 391954136, 2630952180
OFFSET
1,3
FORMULA
a(n) = n * A192508(n). - Joerg Arndt, Jul 03 2011
PROG
(Sage)
def a(n):
ans = 0
for x in GF(5^n):
if x!=0 and x.trace()==0 and x.multiplicative_order()==5^n-1: ans += 1
return ans # Robin Visser, May 10 2024
CROSSREFS
Cf. A192508.
Cf. A192211, A192212, A192214, A192215, A192216 for other primes.
Sequence in context: A045669 A045660 A334307 * A050690 A079561 A328326
KEYWORD
nonn,hard,more
AUTHOR
Pasha Zusmanovich, Jun 25 2011
EXTENSIONS
a(9)-a(11) from Joerg Arndt, Oct 03 2012
a(12)-a(15) from Robin Visser, May 10 2024
STATUS
approved