Probably integrable square wave via sign function

(*Mathematica divergent sum start*)
nn = 20;
(*f[t_]=D[RiemannSiegelTheta[t],t];*)
f[t_] = 1/2 (-Log[2] - Log[\[Pi]] - Log[1/t]);
abs[x_] =
  2/Pi + (4/Pi) Sum[((-1)^(k - 1)/(4 k^2 - 1)) ChebyshevT[2 k, x], {k,
       1, 40}];
inv[x_] = Normal[Series[(1 + x)^(-1), {x, 0, 40}]];
squarewave[
   t_] = (Sign[RiemannSiegelZ[t]]*
     Abs[Zeta[1/2 + I*t]*
        Total[Table[
          Total[MoebiusMu[Divisors[n]]/Divisors[n]^(1/2 + I*t - 1)]/
           n, {n, 1, nn}]]]/(f[t] + HarmonicNumber[nn]))/Pi;
Plot[squarewave[t], {t, 0, 60}, PlotStyle -> Thickness[0.004],
 ImageSize -> Large, PlotRange -> {-1.2, 1.2}]
Plot[squarewave[t]*inv[-1 + abs[squarewave[t]]], {t, 0, 60},
 PlotStyle -> Thickness[0.004], ImageSize -> Large,
 PlotRange -> {-1.2, 1.2}]
(*end*)