A192213 Number of zero trace primitive elements in Galois field GF(5^n).

0, 0, 12, 32, 270, 840, 7812, 23808, 178452, 583880, 4882812, 12434160, 122070312, 391954136, 2630952180

Offset

1,3

Links

Table of n, a(n) for n=1..15.

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

Adjacent sequences: A192210 A192211 A192212 * A192214 A192215 A192216

Keyword

nonn,hard,more,changed

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