Dirichlet divisor problem and Hurwitz zeta function

Clear[a, b, c, n, s, cc];
nn = 100;
(*Limit[Sum[1/k^s,{k,1,n/q}],n->1234]
Limit[Sum[1/k^s,{k,1,q*n}],n->1234]*)
s = N[0, 20];
Clear[n, k, q];
Show[ListPlot[
  A = Table[Re[Sum[Sum[1/k^s, {k, 1, n/q}], {q, 1, n}]], {n, 1, nn}]],
  ListLinePlot[
  B = Table[
    Re[Sum[Zeta[s] - HurwitzZeta[s, n/q + EulerGamma], {q, 1, n}] +
      HarmonicNumber[n, s + 1]/(2 + s)], {n, 1, nn}],
  PlotStyle -> Red]]
ListLinePlot[A - B]


(*start*)
Clear[a, b, c, sigma, n, s, cc];
nn = 100;
a = 2;
b = 4;
c = 5;
Limit[Sum[1/k^s, {k, 1, a*n}], n -> 100]
cc = N[Im[ZetaZero[1]], 30];
sigma = 1/1;
s = sigma + cc*I;
Clear[n];
Show[ListPlot[Table[Re[Sum[1/k^s, {k, 1, a*n}]], {n, 1, nn}]],
 ListLinePlot[
  Table[Re[Zeta[s] - HurwitzZeta[s, a*n + 1]], {n, 1, nn}],
  PlotStyle -> Red]]
Show[ListPlot[Table[Im[Sum[1/k^s, {k, 1, a*n}]], {n, 1, nn}]],
 ListLinePlot[
  Table[Im[Zeta[s] - HurwitzZeta[s, a*n + 1]], {n, 1, nn}],
  PlotStyle -> Black]]
(*end*)

(*start*)
Clear[a, b, c, n, s, cc];
nn = 210;
(*Limit[Sum[1/k^s,{k,1,n/q}],n->2022]
Limit[Sum[1/k^s,{k,1,q*n}],n->2022]*)
s = 0;
Clear[n, k, q];
n1 = 7;
Show[ListPlot[
  A = Table[
    Re[Sum[Sum[1/k^s, {k, 1, n/q}], {q, 1, n1}]], {n, 1, nn}]],
 ListLinePlot[
  B = Table[
    Re[Sum[Zeta[s] - HurwitzZeta[s, n/q + 1], {q, 1, n1}]] - 1/4 -
     2/6 - 3/8 - 4/10 - 5/12 - 6/14, {n, 1, nn}], PlotStyle -> Red]]
ListLinePlot[A - B]
Mean[A - B]
(*end*)

(*start better*)
Clear[a, b, c, n, s, cc];
nn = 200;
(*Limit[Sum[1/k^s,{k,1,n/q}],n->1234]
Limit[Sum[1/k^s,{k,1,q*n}],n->1234]*)
s = 0
Clear[n, k, q, n1];
Show[ListPlot[
  A = Table[Re[Sum[Sum[1/k^s, {k, 1, n/q}], {q, 1, n}]], {n, 1, nn}]],
  ListLinePlot[
  B = Table[
    Re[Sum[Zeta[s] - HurwitzZeta[s, n/q + 1], {q, 1, n}] +
       Sum[(-q + 1)/q/2*(n/q)^(-s), {q, 1, n}]] + n*EulerGamma -
     n/2, {n, 1, nn}], PlotStyle -> Red]]
ListLinePlot[A - B]
(*end better*)