Relation to square roots Linear programming

(*program 1*)
a = 1;
nn = 80;
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}, {-a*(n - 1), 0* (n - 1)}], {n, 1, k}]], {k,
     1, nn}]];
t1 = Table[Sum[If[L2[[n, k]] <= -1, 1, 0], {k, 2, n}], {n, 2, nn}]
t2 = Table[Round[Sqrt[2/a*(n - 1)]], {n, 2, nn}]
t1 - t2
Count[%, 0] - Length[t2]
(*end*)

(*program 2*)
a = 2;
nn = 80;
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}, {-a*(n - 1), 0* (n - 1)}], {n, 1, k}]], {k,
     1, nn}]];
t1 = Table[Sum[If[L2[[n, k]] <= -1, 1, 0], {k, 2, n}], {n, 2, nn}]
t2 = Table[Round[Sqrt[2/a*(n - 1)]], {n, 2, nn}]
t1 - t2
Count[%, 0] - Length[t2]
(*end*)

(*program 3*)
a = 3;
nn = 80;
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}, {-a*(n - 1), 0* (n - 1)}], {n, 1,
       k}]], {k, 1, nn}]];
t1 = Table[Sum[If[L2[[n, k]] <= -1, 1, 0], {k, 2, n}], {n, 2, nn}]
t2 = Table[Round[Sqrt[2/a*(n - 1)]], {n, 2, nn}]
t1 - t2
Count[%, 0] - Length[t2]
(*end*)



(*start*)
Clear[nn];
nn = 12
(*Linear programming problem*)
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, 2, n}], {n, 1, nn}]

(*arithmetic sum*)
TableForm[
B = Table[
Table[If[n <= b, 1, 0]*
Sum[If[Mod[n, k] == 0,
Sum[If[a >= n/k, -If[Mod[a, n/k] == 0, 1 - n/k, 1]*
MoebiusMu[n/k], 0], {a, 1, b}], 0], {k, 1, nn}], {b, 1,
nn}], {n, 1, nn}]]
Total[B]
(*end*)