Modified version Eric Naslunds arithmetic sequence

(*Mathematica start*)
Print["Try changing the power s of matrix A here:"]
nn = 12;
s = 5;
A = Table[Table[If[Mod[n, k] == 0, k, 0], {k, 1, nn}], {n, 1, nn}];
B = Table[
   Table[If[Mod[k, n] == 0, MoebiusMu[n], 0], {k, 1, nn}], {n, 1, nn}];
MatrixForm[MM = MatrixPower[A, s].B];

Clear[t, n, k, M, x];
t[n_, 1] = 0;
t[1, k_] = 0;
t[n_, k_] :=
  t[n, k] =
   If[n < k,
    If[And[n > 1, k > 1], x - Sum[t[k - i, n], {i, 1, n - 1}], 0],
    If[And[n > 1, k > 1], x - Sum[t[n - i, k], {i, 1, k - 1}], 0]];
M = Table[Table[t[n, k], {k, 1, nn}], {n, 1, nn}];
MatrixForm[M];
Print["The roots of the ", s, "-th power of the matrix A"]
(x /. Solve[Det[M + MM] == 0, x])
Print["The modified Eric Naslund formula for the arithmetic sequence"]
Table[MoebiusMu[n]^2*n^s/(n - EulerPhi[n]), {n, 2, nn}]
(*Mathematica end*)



(*Mathematica start*)
nn = 12;
A = Table[Table[If[Mod[n, k] == 0, k, 0], {k, 1, nn}], {n, 1, nn}];
B = Table[
   Table[If[Mod[k, n] == 0, MoebiusMu[n], 0], {k, 1, nn}], {n, 1, nn}];
MatrixForm[M = MatrixExp[MatrixExp[MatrixExp[MatrixExp[A]]]].B];

Clear[t, n, k, x];
t[n_, 1] = 0;
t[1, k_] = 0;
t[n_, k_] :=
  t[n, k] =
   If[n < k,
    If[And[n > 1, k > 1], x - Sum[t[k - i, n], {i, 1, n - 1}], 0],
    If[And[n > 1, k > 1], x - Sum[t[n - i, k], {i, 1, k - 1}], 0]];
T = Table[Table[t[n, k], {k, 1, nn}], {n, 1, nn}];
MatrixForm[T];
Print["The roots of the matrix exponential of the matrix"]
(x /. Solve[Det[M + T] == 0, x])
Print["The modified Eric Naslund formula for the arithmetic sequence"]
Table[MoebiusMu[n]^2*Exp[Exp[Exp[Exp[n]]]]/(n - EulerPhi[n]), {n, 2,
  nn}]
(*Mathematica end*)