Twiddlewood conjecture

(*program 1 start*)
Clear[nn, a, n, d, h, T2, T4, k, m];
nn = 25;
mm = 7;
a[n_] := If[n < 1, 0, Sum[d*MoebiusMu@d, {d, Divisors[n]}]];
h = 2;
TableForm[
 T2 = Table[
   Table[Table[
     If[Mod[n, k] == 0, a[GCD[n/k, m]]*a[GCD[k, m + h]], 0], {k, 1,
      n}], {m, 1, nn}], {n, mm, mm}]]
h = 4;
TableForm[
 T4 = Table[
   Table[Table[
     If[Mod[n, k] == 0, a[GCD[n/k, m]]*a[GCD[k, m + h]], 0], {k, 1,
      n}], {m, 1, nn}], {n, mm, mm}]]
(*program 1 end*)

(*program 2 start*)
Clear[nn, a, n, d, h, T2, T4, k, m, mm];
TableForm[Table[
  nn = mm;
  a[n_] := If[n < 1, 0, Sum[d*MoebiusMu@d, {d, Divisors[n]}]];
  TableForm[{Table[{n, a[n]}, {n, 1, mm}]}];
  TableForm[{aa = Table[{n, a[GCD[n, mm]]}, {n, 1, mm}]}];
  h = 2;
  TableForm[
   T2 = Table[
     Table[Table[
       If[Mod[n, k] == 0, a[GCD[n/k, m]]*a[GCD[k, m + h]], 0], {k, 1,
        n}], {m, 1, nn}], {n, mm, mm}]];
  TableForm[
   bb2 = mm - Sort[Position[T2, aa[[mm, 2]]], #1[[3]] < #2[[3]] &]];
  h = 4;
  TableForm[
   T4 = Table[
     Table[Table[
       If[Mod[n, k] == 0, a[GCD[n/k, m]]*a[GCD[k, m + h]], 0], {k, 1,
        n}], {m, 1, nn}], {n, mm, mm}]];
  TableForm[
   bb4 = mm - Sort[Position[T4, aa[[mm, 2]]], #1[[3]] < #2[[3]] &]];
  {mm, Length[bb2 - bb4], {bb4 - bb2}}, {mm, 1, 100}]]
(*program 2 end*)