(*start*)
nn = 50;
g1 = Plot[
   Re[Sum[Zeta[1/2 + I*t]*
      Total[MoebiusMu[Divisors[n]]/Divisors[n]^(1/2 + I*t - 1)]/n/
       t, {n, 1, nn}]], {t, 0, 60}, PlotStyle -> Thickness[0.005]];
f[t_] = D[RiemannSiegelTheta[t], t];
g2 = Plot[(f[t] + HarmonicNumber[nn])/t, {t, 0, 60},
   PlotRange -> {0, 1}, PlotStyle -> {Thickness[0.004], Red}];
Show[g1, g2, ImageSize -> Large]
(*end*)

(*start*)
f[t_] = D[RiemannSiegelTheta[t], t];
nnn = 60
cc = 10;
g1 = Plot[(f[t] + cc + EulerGamma), {t, 0, nnn},
   PlotStyle -> {Thickness[0.004], Red}, PlotRange -> {-2, cc + 5}];
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 + 5}, PlotStyle -> Thickness[0.02]];
Show[g2, g1, ImageSize -> Large]
(*end*)