A192214 Number of zero trace primitive elements in Galois field GF(7^n).

0, 0, 9, 80, 800, 5076, 37982, 218880, 1770660, 12155480, 94076488, 447960240

Offset: 1

Author

Pasha Zusmanovich, Jun 25 2011

Keywords

• nonn
• hard
• more

Crossrefs

Cf. A192211, A192212, A192213, A192215, A192216 for other primes.

Cf. A192509.

Programs

Sage

def a(n):
    ans = 0
    for x in GF(7^n):
        if x!=0 and x.trace()==0 and x.multiplicative_order()==7^n-1: ans += 1
    return ans  # Robin Visser, Jun 01 2024

Formula

a(n) = n * A192509(n). - Joerg Arndt, Jul 03 2011

Extensions

a(7)-a(9) added using the data at A192509 by Amiram Eldar, May 03 2024

a(10)-a(12) from Robin Visser, Jun 01 2024