Liouville Lambda approximation

(*Mathematica 8.0.1 start*)
Monitor[Table[
  Clear[A, a, n, k, nn, q, Q];
  nn = 800;
  numberOfColumns =
   num;(*Increase this number for better precision of the Liouville \
Lambda function*)
  q = Table[Sum[If[n == k^2, k, 0], {k, 1, Sqrt[n]}], {n, 1, nn}];
  a[n_] := Total[Divisors[n]*MoebiusMu[Divisors[n]]];
  Monitor[
    A = Table[
       If[n == 1, 0,
        Sum[-1*a[GCD[n, k]]/N[k]/Log[n] +
          Sign[q[[n]]]*a[GCD[q[[n]], k]]/k/Log[q[[n]]], {k, 1,
          numberOfColumns}]], {n, 1, nn}];, n]
   "ListPlot[approximatedLiouvilleLambda] in blue vs \
ListPlot[LiouvilleLambda] in red";
  Show[ListPlot[
    approximatedLiouvilleLambda = (MatrixExp[
        Table[Table[If[Mod[n, k] == 0, A[[n/k]], 0], {k, 1, nn}], {n,
          1, nn}]])[[All, 1]], Filling -> 0],
   ListPlot[LiouvilleLambda[Range[nn]], PlotStyle -> Red]];
  "approximatedLiouvilleLambda";
  Flatten[
    Position[
     Abs[Sign[
       Sign[N[approximatedLiouvilleLambda]] -
        LiouvilleLambda[Range[nn]]]], 1]][[1]], {num, 1, 10}], num]
(*Mathematica 8.0.1 end*)