Combinatorial approach to linear programming problem

(*start*)
Clear[A, B, a];
nn = 7;
B = Table[
   Tuples[Table[
     Table[If[k == 1, m, n], {n, -(k - 1), k - 1}], {k, 1, m}]], {m,
    1, nn}];
B1 = Table[
   DeleteCases[
    Table[If[Total[B[[n, k]]] == 1, B[[n, k]], a], {k, 1,
      Length[B[[n]]]}], a], {n, 1, nn}];

Clear[T, n, k, a];
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, 1,
      nn}], {m, 1, nn}]];
M1 = Table[Table[M[[n, k]], {k, 1, n}], {n, 1, nn}] ;
Table[Flatten[Position[B, M1[[n]]]][[2]], {n, 1, nn}]
Table[Flatten[Position[B1, M1[[n]]]][[2]], {n, 1, nn}]
(*end*)