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A054662
Number of monic irreducible polynomials over GF(5) with fixed nonzero trace.
5
1, 2, 8, 30, 125, 516, 2232, 9750, 43400, 195250, 887784, 4068740, 18780048, 87191964, 406901000, 1907343750, 8975758272, 42385503300, 200773540296, 953674218750, 4541306267856, 21674415838068, 103660251783288
OFFSET
1,2
COMMENTS
Also number of 5-ary Lyndon words with trace 1 mod 5; trace 2 mod 5; trace 3 mod 5; trace 4 mod 5; also number of 5-ary Lyndon words of trace 1 over GF(5), trace 2 over GF(5); trace 3 over GF(5); trace 4 over GF(5).
FORMULA
a(n) = 1/(5*n) * Sum_{d|n, gcd(d,5)=1} mu(d) * 5^(n/d). - Seiichi Manyama, May 29 2024
PROG
(PARI) a(n) = sumdiv(n, d, (gcd(d, 5)==1)*(moebius(d)*5^(n/d)))/(5*n); \\ Seiichi Manyama, May 29 2024
CROSSREFS
Column 5 of A110540.
Sequence in context: A074026 A054663 A150763 * A150764 A150765 A150766
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Apr 18 2000
EXTENSIONS
More terms from James A. Sellers, Apr 19 2000
STATUS
approved