OFFSET
1,1
COMMENTS
Number of monic irreducible polynomials of degree n over GF(11). # Robert Israel, Jan 07 2015
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..500
C. G. Bower, Transforms (2)
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc. [Cached copy, with permission, pdf format only]
FORMULA
"CHK" (necklace, identity, unlabeled) transform of 11, 0, 0, 0...
a(n) = Sum_{d|n} mu(d)*11^(n/d)/n.
G.f.: Sum_{k>=1} mu(k)*log(1/(1 - 11*x^k))/k. - Ilya Gutkovskiy, May 19 2019
MAPLE
f:= (n, p) -> add(numtheory:-mobius(d)*p^(n/d), d=numtheory:-divisors(n))/n:
seq(f(n, 11), n=1..100); # Robert Israel, Jan 07 2015
MATHEMATICA
f[d_]:=MoebiusMu[d] 11^(n/d)/n; a[n_]:=Total[f/@Divisors[n]]; a[0]=1; Table[a[n], {n, 1, 30}] (* Vincenzo Librandi, Oct 14 2017 *)
PROG
(PARI) a(n) = sumdiv(n, d, moebius(d)*11^(n/d))/n; \\ Michel Marcus, Jan 07 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved