How can I integrate this zeta function expression?

Question

Can you integrate this function:

$$f(k)=\exp\left(-\Re\left(\sum\limits_{n=1}^{n=scale} \frac{1}{n} \zeta(1/2+i \cdot k)\sum\limits_{d|n} \frac{\mu(d)}{d^{(1/2+i \cdot k-1)}}\right)\right)$$

with respect to $k$?

The result I would like to achieve is the plot from the accumulated function as in this Mathematica program:

(*program start*)
scale = 300;
Print["Counting to 60"]
Monitor[g1 = 
   ListLinePlot[
    0.69*Accumulate[
      Table[Exp[-Re[
          Zeta[1/2 - I*k]*
           Total[Table[
             Total[MoebiusMu[Divisors[n]]/
                Divisors[n]^(1/2 - I*k - 1)]/n, {n, 1, scale}]]]], {k,
         0 + 1/1000, 60, N[1/6]}]], DataRange -> {0, 60}, 
    PlotRange -> {-0.15, 15}];, Floor[k]]
Show[g1, ListPlot[Table[{N[Im[ZetaZero[n]]], n}, {n, 1, 13}], 
  PlotStyle -> Black, Filling -> Axis]]
(*program end*)

The function jumps about one unit at $k$ values equal to zeta zeros.