The Liouville function

(* Mathematica 8.0.1 *)
(*start*)
nn = 15;
Table[Sum[If[a^2 == n, 1, 0], {a, 1, nn}] -
  Sum[Sum[If[a^2*b == n, 1, 0], {a, 1, nn}], {b, 2, nn}] +
  Sum[Sum[Sum[If[a^2*b*c == n, 1, 0], {a, 1, nn}], {b, 2, nn}], {c, 2,
     nn}] - +Sum[
    Sum[Sum[Sum[If[a^2*b*c*d == n, 1, 0], {a, 1, nn}], {b, 2,
       nn}], {c, 2, nn}], {d, 2, nn}], {n, 1, nn}]
LiouvilleLambda[Range[nn]]
%% - %
(*end*)