Clear[a, b, nn];
nn = 60;
a[n_] := Total[MoebiusMu[Divisors[n]]*Divisors[n]];
Monitor[a1 =
Table[Sum[Sum[a[GCD[m, r]], {m, r, n}]/r, {r, 2, n}], {n, 1,
nn}];, n]
g1 = ListLinePlot[a1, PlotStyle -> {Red, Thick}];
Monitor[a2 =
Table[Sum[
If[Sum[-Abs[Sum[a[GCD[m, k]], {m, k, n}]], {k, 2,
r}] >= -(n - 1), -Abs[Sum[a[GCD[m, r]], {m, r, n}]]/r,
0], {r, 2, n}], {n, 1, nn}];, n]
g2 = ListLinePlot[a2, PlotStyle -> {Thick}];
Show[g2, g1]