Square root bound subsets of the summatory von Mangoldt

(*Numerators of the partial sums of the Möbius inverse of the \
Harmonic numbers*)(*start*)
Clear[T, n, k, a];
nn = 80;
mm = 14
a[n_] := If[n < 1, 0, Sum[d MoebiusMu@d, {d, Divisors[n]}]]
TableForm[
  M = Table[
    Table[Sum[If[n >= k, a[GCD[n, k]], 0], {n, 1, m}]/(k - mm), {k,
      1 + mm, nn}], {m, 1, nn}]];
TableForm[
  Table[Table[If[M[[n, k]] == -1, 1, 0], {k, 1, n}], {n, 1, nn - mm}]];
Sign[Sum[Table[If[M[[n, k]] == -1, 1, 0], {k, 1, nn - mm}], {n, 1,
   nn - mm}]]
Flatten[Position[%, 1]]
Select[Range[900], PrimeQ[# + mm] &][[-1 + Range[Length[%]]]]
%% - %