Constraints giving the von Mangoldt function matrix

(*mathematica*)nn = 12;
TableForm[A = Table[Table[a[n, k], {k, 1, nn}], {n, 1, nn}]]
"Constraints"
TableForm[
 RowSums =
  Table[Table[
    Sum[A[[r, m]], {m, k, k + r - 1}] == If[r == 1, 1, 0], {k, 1,
     nn - (r - 1)}], {r, 1, nn}]]
TableForm[
 ColumnSums =
  Table[Table[
    Sum[A[[m, r]], {m, k, k + r - 1}] == If[r == 1, 1, 0], {k, 1,
     nn - (r - 1)}], {r, 1, nn}]]
Constraints = Flatten[{RowSums, ColumnSums}];
Constraints1 =
  StringJoin[
   Table[StringJoin[ToString[Constraints[[n]]], " && "], {n, 1,
     Length[Constraints]}]];
Variables1 = Flatten[A];
Variables2 = ToString[Flatten[A]];
VariablesAreIntegers =
  StringJoin[
   Table[StringJoin[ToString[Variables1[[n]]],
     " \[Element] Integers ",
     If[n == Length[Variables1], "", " && "]], {n, 1,
     Length[Variables1]}]];
"KnapsackConstraint"
KnapsackConstraint =
  ToString[Total[
    Total[Table[
      Sum[Table[
        StringJoin[ToString[If[n >= k, A[[n, k]], 0]]], {k, 1,
         nn}], {n, 1, mm}], {mm, nn, nn}]]]];
KnapsackConstraint = StringJoin[ToString[KnapsackConstraint], "==1"]
"VariableBounds"
"ObjectiveFunction"
ObjectiveFunction =
 ToString[Total[
   Total[Table[
     Sum[Table[
       StringJoin[ToString[If[n >= k, A[[n, k]], 0]], "/",
        ToString[k]], {k, 1, nn}], {n, 1, mm}], {mm, nn, nn}]]]]
TableForm[
 Table[Sum[
   Table[If[n >= k, A[[n, k]], 0]/k, {k, 1, nn}], {n, 1, mm}], {mm,
   nn, nn}]]
ab = StringJoin["FindMaximum[{", ObjectiveFunction, " , ",
   KnapsackConstraint, Constraints1, VariablesAreIntegers, "},",
   Variables2, "]"];
"Solution"
Solution =
  ReleaseHold[MakeExpression[RowBox[{ab}], StandardForm]][[2]];
TableForm[
  Table[Table[Solution[[n]], {n, (k - 1)*nn + 1, k*nn}], {k, 1, nn}]];
TableForm[
 Table[Table[
   First[Solution[[n]]] /. Solution[[n]], {n, (k - 1)*nn + 1,
    k*nn}], {k, 1, nn}]]
(*end*)