Modelling the back bone of zeta zero spectrum comb

(*start*)
f[t_] = D[RiemannSiegelTheta[t], t]
nnn = 60
cc = 2; (*set "cc" to 0.000000000000001 to get the Riemann zeta \
function on the criticl line*)
g1 = Plot[(f[t] + cc + EulerGamma), {t, 0, nnn},
  PlotStyle -> {Thickness[0.004], Red}, PlotRange -> {-2, cc + 10}];
c = 1 + 1/cc;
g2 = Plot[
   Re[Zeta[1/2 + I*t]*Zeta[c]/Zeta[1/2 + I*t + c - 1]], {t, 0, nnn},
   PlotRange -> {-2, cc + 10}, PlotStyle -> Thickness[0.02]];
Show[g2, g1, ImageSize -> Large]
N[Re[Zeta[1/2 + I*5]*Zeta[c]/Zeta[1/2 + I*5 + c - 1]], 30]
(*end*)

(*start*)
scale = 50;(*scale=5000 gives the plot below*)
Print["Counting to 60"]
Monitor[g1 =
   ListLinePlot[
    Table[Re[
      Zeta[1/2 + I*k]*
       Total[Table[
         Total[MoebiusMu[Divisors[n]]/Divisors[n]^(1/2 + I*k - 1)]/(n*
            k), {n, 1, scale}]]], {k, 0 + 1/1000, 60, N[1/6]}],
    DataRange -> {0, 60}, PlotRange -> {-0.15, 1.5}], Floor[k]];
f[t_] = D[RiemannSiegelTheta[t], t];
g2 = Plot[f[t]/t + HarmonicNumber[scale]/t, {t, 0, 60}, PlotStyle -> Red];
Show[g1, g2]
(*end*)