Is this wave noisy at prime powers and silent at composite numbers?

Question

Mathematica knows that:

$$\log(n) = \lim\limits_{s \rightarrow 1} \zeta(s)\left(1 - \frac{1}{n^{(s - 1)}}\right)$$

And the von Mangoldt function should then be:

$$\Lambda(n)=\lim\limits_{s \rightarrow 1} \zeta(s)\sum\limits_{d|n} \frac{\mu(d)}{d^{(s-1)}}$$

I do not know what the zeros of $\zeta(s)$ are, but the divisor part has zeros with real part equal to one:

$$\text{frequencies }z = 1+\frac{2 i \pi k}{\Lambda (n)}$$

where $k$ is integer, and $\Lambda (n)$ is the von Mangoldt function.

Mathematica:

TableForm[
 Table[{n, 
   Reduce[Total[MoebiusMu[Divisors[n]]/Divisors[n]^(s - 1)] == 0, 
    s]}, {n, 1, 29}]]

The question is if this wave is silent at composite numbers and noisy at prime powers?

The program and the plot (and question also) are still half baked and I need to improve on parameters in the frequencies in the program.

The waves are of the form $$\Re\left(n^{z_i}\right)$$

Mathematica:

Clear[n, k, A, a, B, b, kk, ii, i]
(*kk=50;(*number of Zeta zeros used*)*)
ii = 10;(*reciprocal of x-axis spacing*)
n = Table[i, {i, 0, 42, 1/ii}];
Monitor[z = 
   DeleteCases[
    Flatten[Table[
      Table[1 + (2 I \[Pi]*k)/MangoldtLambda[n], {n, 1, 42}], {k, 1, 
       4*42}]], ComplexInfinity];, k]
kk = Length[z]
Monitor[A = -Table[Re[n^N[z[[k]], 12]], {k, 1, kk}];, k]
Monitor[a = Table[{-i/ii, Plus @@ A[[All, i]]}, {i, 1, Length[n]}];, i]
(*a[[ii+1]]={-(ii+1)/ii,0};*)
(*ListLinePlot[-a,PlotRange->{-2000,12000}]*)

g1 = ListLinePlot[-a, PlotRange -> {-2000, 12000}, 
   Ticks -> {Range[42], {-2000, 12000}}];
g2 = Table[
   Graphics[Line[{{N[n] + 1/10, 3000}, {N[n] + 1/10, 12000}}]], {n, 1,
     42}];
Show[g1]

The ticks at the x-axis in the plot are off position by $\frac{1}{10}$ due to the programming.

---

Edit 25 2 2014:

Clear[n, k, A, a, B, b, kk, ii, i]
(*kk=50;(*number of Zeta zeros used*)*)
ii = 10;(*reciprocal of x-axis spacing*)
n = Table[i, {i, 0, 42, 1/ii}];
Monitor[z = 
   DeleteCases[
    Flatten[Table[
      Table[1/2 + (2 I \[Pi]*k)/Log[Prime[n]], {n, 1, 42}], {k, 1, 
       3*42}]], ComplexInfinity];, k]
kk = Length[z]
Monitor[A = -Table[Re[n^N[z[[k]], 12]], {k, 1, kk}];, k]
Monitor[a = Table[{-i/ii, Plus @@ A[[All, i]]}, {i, 1, Length[n]}];, i]
(*a[[ii+1]]={-(ii+1)/ii,0};*)
(*ListLinePlot[-a,PlotRange->{-2000,12000}]*)

g1 = ListLinePlot[-a, PlotRange -> {-300, 800}, 
   Ticks -> {Range[42], {-300, 500}}];
g2 = Table[
   Graphics[Line[{{N[n] + 1/10, 3000}, {N[n] + 1/10, 12000}}]], {n, 1,
     42}];
Show[g1]

Clear[n, k, A, a, B, b, kk, ii, i]
ii = 10;(*reciprocal of x-axis spacing*)
n = Table[i, {i, 0 + 1/ii, 42, 1/ii}];
Monitor[z = 
   DeleteCases[
    Flatten[Table[
      Table[Table[(2 I \[Pi]*k)/Log[Prime[n]], {p, 1, n}], {n, 1, 
        13}], {k, 1, 2*42}]], ComplexInfinity];, k]
kk = Length[z]
Print["1"]
Monitor[A = -Table[Re[n^N[z[[k]], 12]], {k, 1, kk}];, k]
Print["2"]
Monitor[a = Table[{-i/ii, Plus @@ A[[All, i]]}, {i, 1, Length[n]}];, i]
Print["3"]
g1 = ListLinePlot[-a, PlotRange -> {-500, 1500}, 
   Ticks -> {Range[42], {-500, 1500}}];
Print["4"]
g2 = Table[
   Graphics[Line[{{N[n] + 1/10, 3000}, {N[n] + 1/10, 12000}}]], {n, 1,
     42}];
Show[g1, ImageSize -> Large]