Linear progamming and minimum bound

Clear[t, n, k];
nn = 101;
t[n_, 1] = 1;
t[1, k_] = 1;
t[n_, k_] :=
  t[n, k] =
   If[n > k, -Sum[t[n - i, k], {i, 1, k - 1}], -Sum[
      t[n, k - i], {i, 1, n - 1}]];
TableForm[
  A = Accumulate[
    Table[Table[If[n >= k, t[n, k], 0], {k, 1, nn}], {n, 1, nn*2}]]];
max = Table[Max[A[[All, k]]], {k, 1, nn}]
min = Table[Min[A[[All, k]]], {k, 1, nn}]
Flatten[Position[Sign[max], 1]]
max + min
maxANDmin = Table[If[max[[n]] > 0, max[[n]], min[[n]]], {n, 1, nn}]
min == min
min[[1]] = 1;

Clear[a, b];
nn = nn - 1;
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[min[[k]], {k, 2, r}] + (n - 1) >= 0, min[[r]]/r, 0], {r,
       2, n}] +
     Sum[If[And[Sum[min[[k]], {k, 2, r}] + (n - 1) >= 0,
        Sum[min[[k + 1]], {k, 2, r}] + (n - 1) <=
         0], -(Sum[min[[k]], {k, 2, r}] + (n - 1))/(r), 0], {r, 2,
       n}], {n, 1, nn}];, n]
g2 = ListLinePlot[a2, PlotStyle -> {Thick}];
g3 = Show[g2, g1]
Sign[a2 - a1]
Length[%]
Count[%%, -1]
Position[%%%, 1]

(*start*)
TableForm[
  L2 = Table[
    LinearProgramming[
     Table[1/n, {n, 1, k}], {Table[If[n == 1, k, 1], {n, 1, k}]}, {{1,
        0}}, Table[
      If[n == 1, {-1, 1}, {-2*(n - 1), 0 (n - 1)}], {n, 1, k}]], {k,
     1, nn}]];
t1 = Table[Sum[L2[[n, k]]/k, {k, 2, n}], {n, 2, nn}];
t2 = Table[-(2*k^(1/2) + 1 - 2*Log[k^(1/2) + 1] - 2*EulerGamma), {k,
    2, nn}];
Show[ListLinePlot[t1], g3]