"Dirichlet series" for log(log(n))

(*Matheamtica start*)
LL = 19;
Monitor[TableForm[numerator = Table[Clear[nn, loglog, s];
    $MaxPrecision = 100;
    s = s;
    nn = LL;
    loglog = L;
    TableForm[
     Z = Table[
       Table[If[Mod[n, k] == 0, 1/(n/k)^s, 0], {k, 1, nn}], {n, 1,
        nn}]];
    TableForm[
     A = Table[
        Table[If[n/k == loglog, -loglog/(n/k)^s, 0], {k, 1, nn}], {n,
         1, nn}] + IdentityMatrix[nn]];
    (*TableForm[Z.A];*)
    generatingFunction = -(Zeta[
         s] ((IdentityMatrix[nn] - MatrixPower[(Z.A), s - 1])[[All,
          1]]));
    limit = Limit[generatingFunction, s -> 1];
    accumulate = Accumulate[limit];
    cesaro = N[Total[accumulate]/Length[accumulate], 30];
    Numerator[limit], {L, 1, LL}]], L]

LL = 19;
Monitor[TableForm[denominator = Table[Clear[nn, loglog, s];
    $MaxPrecision = 100;
    s = s;
    nn = LL;
    loglog = L;
    TableForm[
     Z = Table[
       Table[If[Mod[n, k] == 0, 1/(n/k)^s, 0], {k, 1, nn}], {n, 1,
        nn}]];
    TableForm[
     A = Table[
        Table[If[n/k == loglog, -loglog/(n/k)^s, 0], {k, 1, nn}], {n,
         1, nn}] + IdentityMatrix[nn]];
    (*TableForm[Z.A];*)
    generatingFunction = -(Zeta[
         s] ((IdentityMatrix[nn] - MatrixPower[(Z.A), s - 1])[[All,
          1]]));
    limit = Limit[generatingFunction, s -> 1];
    accumulate = Accumulate[limit];
    cesaro = N[Total[accumulate]/Length[accumulate], 30];
    Denominator[limit], {L, 1, LL}]], L]
TableForm[ratio = numerator/denominator]
TableForm[
 logTable =
  Table[Table[If[Mod[k, n] == 0, 1 - n, 1]/k, {k, 1, nn}], {n, 1, nn}]]
TableForm[ratio = Range[Length[denominator]]*numerator/denominator]
TableForm[ratio + logTable]
TableForm[Floor[ratio + logTable]]
(*end*)

(*start*)
LL = 19;
Monitor[TableForm[numerator = Table[Clear[nn, loglog, s];
    $MaxPrecision = 100;
    s = s;
    nn = LL;
    loglog = L;
    TableForm[
     Z = Table[
       Table[If[Mod[n, k] == 0, 1/(n/k)^s, 0], {k, 1, nn}], {n, 1,
        nn}]];
    TableForm[
     A = Table[
        Table[If[n/k == loglog, -loglog/(n/k)^s, 0], {k, 1, nn}], {n,
         1, nn}] + IdentityMatrix[nn]];
    (*TableForm[Z.A];*)
    generatingFunction = -(Zeta[
         s] ((IdentityMatrix[nn] - MatrixPower[(Z.A), s - 1])[[All,
          1]]));
    limit = Limit[generatingFunction, s -> 1];
    accumulate = Accumulate[limit];
    cesaro = N[Total[accumulate]/Length[accumulate], 30];
    Numerator[limit], {L, 1, LL}]], L]

LL = 19;
Monitor[TableForm[denominator = Table[Clear[nn, loglog, s];
    $MaxPrecision = 100;
    s = s;
    nn = LL;
    loglog = L;
    TableForm[
     Z = Table[
       Table[If[Mod[n, k] == 0, 1/(n/k)^s, 0], {k, 1, nn}], {n, 1,
        nn}]];
    TableForm[
     A = Table[
        Table[If[n/k == loglog, -loglog/(n/k)^s, 0], {k, 1, nn}], {n,
         1, nn}] + IdentityMatrix[nn]];
    (*TableForm[Z.A];*)
    generatingFunction = -(Zeta[
         s] ((IdentityMatrix[nn] - MatrixPower[(Z.A), s - 1])[[All,
          1]]));
    limit = Limit[generatingFunction, s -> 1];
    accumulate = Accumulate[limit];
    cesaro = N[Total[accumulate]/Length[accumulate], 30];
    Denominator[limit], {L, 1, LL}]], L]
TableForm[ratio = numerator/denominator]
TableForm[
 logTable =
  Table[Table[If[Mod[k, n] == 0, 1 - n, 1]/k, {k, 1, nn}], {n, 1, nn}]]
TableForm[ratio = Range[Length[denominator]]*numerator/denominator]
TableForm[ratio + logTable]
TableForm[ttable = (ratio + logTable)*3]
TableForm[
 divisorTable =
  Table[Table[If[Mod[k, n] == 0, n, 0], {k, 1, nn}], {n, 1, nn}]]
TableForm[ttable - divisorTable]
TableForm[endTable = (ttable - Transpose[divisorTable])]
TableForm[Floor[1/2 + ttable - Transpose[divisorTable]]]
endTable[[1, 1]] = 0;
Total[endTable]
Total[Transpose[endTable]]
Total[Total[endTable]]
(*end*)