OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
A. Knopfmacher and R. Warlimont, Distinct degree factorizations for polynomials over a finite field, Trans. Amer. Math. Soc. 347 (1995), no. 6, 2235-2243.
FORMULA
G.f.: Product_{m>=1} (1 + pi(m) x^m), where pi(m) = A001037(m) = number of distinct irreducible polynomials of degree m.
EXAMPLE
a(3)=4 from x^3+x+1, x^3+x^2+1, x(x^2+x+1), (x+1)(x^2+x+1).
MATHEMATICA
max = 31; pi[n_] := Total[ MoebiusMu[n/#] * (2^#/n)& /@ Divisors[n]]; f[x_] := Product[ 1+pi[n]*x^n, {n, 1, max}]; CoefficientList[ Series[ f[x], {x, 0, max}], x] (* Jean-François Alcover, Nov 24 2011 *)
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
More terms from David W. Wilson.
STATUS
approved