Mobius function times n approximately as eigenvalues

(*Mathematica 8 program start*)
(*The Mobius function times "n" approximately as the eigenvalues of a matrix*)
Clear[nn, n, k, d, kolumn]
a[n_] := If[n < 1, 0, Sum[d MoebiusMu@d, {d, Divisors[n]}]]
Do[nn = j;
 A3 = Range[nn]*0;
 Do[kolumn = i;
   A1 = Table[Table[a[GCD[n, k]], {k, 1, nn}], {n, 1, nn}];
   MatrixForm[A1];
   A1[[All, kolumn]];
   MatrixForm[
    Table[Table[
      If[Mod[n, k] == 0, MoebiusMu[n/k]*A1[[All, kolumn]][[k]],
       0], {k, 1, nn}], {n, 1, nn}]];
   a1 = Table[
     Total[Table[
       If[Mod[n, k] == 0, MoebiusMu[n/k]*A1[[All, kolumn]][[k]],
        0], {k, 1, nn}]], {n, 1, nn}];
   a2 = Sign[a1]*Exp[Exp[Abs[a1]]];
   A2 = Table[
     Table[If[Mod[n, k] == 0, a2[[n/k]], 0], {k, 1, nn}], {n, 1, nn}];
   MatrixForm[A2];
   a3 = Table[
     Total[Table[If[Mod[n, k] == 0, a2[[n/k]], 0], {k, 1, nn}]], {n,
      1, nn}];
   A3[[i]] = a3;, {i, 1, nn}]
  MatrixForm[A3];
 (*Print[N[Log[Log[-Min[Eigenvalues[A3]]]],12]]*)
 Print[N[Sign[Eigenvalues[A3]] Log[Log[Abs[Eigenvalues[A3]]]],
   12]], {j, 1, 13}]
(*program end*)