More efficient program for square root bounded sequence

(*start*)
a[n_] := Total[MoebiusMu[Divisors[n]]*Divisors[n]]
nn = 1000;
aa = Table[a[n], {n, 1, nn}];
Clear[a];
A = Table[
   Table[If[n >= k, aa[[GCD[n, k]]], 0], {k, 1, nn}], {n, 1, nn}];
Clear[aa];
TableForm[B = -Abs[Accumulate[A]]];
B[[All, 1]] = 0;
Clear[A];
TableForm[G = Transpose[Accumulate[Transpose[B]]]];
Clear[B];
TableForm[H = Sign[(1 + Sign[(G + Range[nn])])]];
Clear[G];
g1 = ListLinePlot[
  b = -Total[
     Transpose[Transpose[Transpose[H]*(Range[nn] - 1)/Range[nn]]]]]
g2 = ListLinePlot[
  4*Accumulate[
    Table[Sum[
       If[Mod[n, k] == 0, MoebiusMu[n/k]*HarmonicNumber[k], 0], {k, 1,
         n}] - 1, {n, 1, nn}]]]
Show[g1, g2]
Clear[H];
ListLinePlot[-b/Sqrt[Range[nn]], PlotRange -> {0, 4}]
(*end*)