Sum of eigenvalues of matrices A and B equal C

(*start*)
(*Mathematica 8.0.1*)
Clear[C1, C2, A, B, s, nn, i];
mm = 32;

"Counts to 32"
t = 1;
Monitor[Table[
  A = Table[
     Table[If[Mod[n, t*k] == 0, Exp[Exp[Exp[1]]], 0], {k, 1, nn}], {n,
       1, nn}].Table[
     Table[If[Mod[k, t*n] == 0, MoebiusMu[n], 0], {k, 1, nn}], {n, 1,
      nn}];
  a = Eigenvalues[A];
  N[Sum[Sign[a[[i]]] If[a[[i]] == 0, 0,
      Log[Log[Log[Abs[a[[i]]]]]]], {i, 1, nn}], 6], {nn, 1, mm}], nn]
sumA = Round[%]

"Counts to 32"
t = 2;
Monitor[Table[
  B = Table[
     Table[If[Mod[n, t*k] == 0, Exp[Exp[Exp[1]]], 0], {k, 1, nn}], {n,
       1, nn}].Table[
     Table[If[Mod[k, t*n] == 0, MoebiusMu[n], 0], {k, 1, nn}], {n, 1,
      nn}];
  b = Eigenvalues[B];
  N[Sum[Sign[b[[i]]] If[b[[i]] == 0, 0,
      Log[Log[Log[Abs[b[[i]]]]]]], {i, 1, nn}], 6], {nn, 1, mm}], nn]
sumB = Round[%]

"Counts to 32"
C1 = A + B;
Monitor[Table[C2 = Table[Table[C1[[n, k]], {k, 1, nn}], {n, 1, nn}];
  c = Eigenvalues[C2];
  N[Sum[Sign[c[[i]]] If[c[[i]] == 0, 0,
      Log[Log[Log[Abs[c[[i]]]]]]], {i, 1, nn}], 6], {nn, 1, mm}], nn]
sumC1 = Round[%]

sumA + sumB
Sum[Table[
  Sum[If[Mod[n, k] == 0, MoebiusMu[n/k], 0], {n, 1, nn}], {nn, 1,
   mm}], {k, 1, t}]
%%% - %%
%%% - %%

t = 1;
muA = Table[
  Sum[If[Mod[n, t] == 0, MoebiusMu[n/t], 0], {n, 1, nn}], {nn, 1, mm}]
t = 2;
muB = Table[
  Sum[If[Mod[n, t] == 0, MoebiusMu[n/t], 0], {n, 1, nn}], {nn, 1, mm}]
muC = muA + muB
(*end*)