A192216 Number of zero trace primitive elements in Galois field GF(13^n).

0, 0, 54, 448, 9520, 103104, 1608936, 13488064, 267423822

Offset: 1

Author

Pasha Zusmanovich, Jun 25 2011

Keywords

• nonn
• hard
• more

Crossrefs

Cf. A192211, A192212, A192213, A192214, A192215 for other primes.

Cf. A192511.

Programs

Sage

def a(n):
    ans = 0
    for x in GF(13^n):
        if x!=0 and x.trace()==0 and x.multiplicative_order()==13^n-1: ans += 1
    return ans  # Robin Visser, Jun 01 2024

Formula

a(n) = n * A192511(n). - Joerg Arndt, Jul 03 2011

Extensions

a(6) added using the data at A192511 by Amiram Eldar, May 03 2024

a(7)-a(9) from Robin Visser, Jun 01 2024