|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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).
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|