von Mangoldt Dirac comb mimic 0.500000000000000000000000000000 + 0.220635600152651593396456432118 I

TableForm[Table[Clear[nn, t, n, k, M, x];
   nn = mm;
   t[n_, 1] = 1;
   t[1, k_] = 1;
   t[n_, k_] :=
    t[n, k] =
     If[n < k,
      If[And[n > 1, k > 1],
       I*Exp[-I*x*Pi] - Sum[t[k - i, n], {i, 1, n - 1}], 0],
      If[And[n > 1, k > 1],
       I*Exp[-I*x*Pi] - Sum[t[n - i, k], {i, 1, k - 1}], 0]];
   M = Table[Table[t[n, k], {k, 1, nn}], {n, 1, nn}];
   MatrixForm[M];
   Det[M]; x /. Solve[Det[M] == 0, x], {mm, 2, 12}]];
MatrixForm[M];
N[%%, 30]



(*Mathematica 8*)
Clear[x, xx]
scale = 200;
xres = .001;
x = Exp[Range[0, Log[scale], xres]];
xx = Flatten[{0, Differences[Floor[Exp[Range[0, Log[scale], xres]]]]}];
yy = Accumulate[xx]*xx;
zz = Table[
   If[yy[[i]] == 0, 0, MangoldtLambda[yy[[i]]]], {i, 1, Length[yy]}];
ListLinePlot[zz*x^(-1), PlotRange -> {-0.1, 0.8}, ImageSize -> Large]
ListLinePlot[Accumulate[zz*x^(-1)], ImageSize -> Large]
Graphics[Line[{{Log[2], Min[Accumulate[zz*x^(-1)]]}, {Log[scale],
    Max[Accumulate[zz*x^(-1)]]}}]]
(*end*)