Powers of matrix A and Eric Naslunds answer

(*Mathematica start*)
 Print["Try changing the power of matrix A here:"]
 power = 2
 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[MM = MatrixPower[A, power].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 ", power, "-d powers of the matrix"]
 N[(x /. Solve[Det[M + MM] == 0, x] )]
 Print["Eric Naslunds formula for the arithmetic sequence"]
 N[Table[MoebiusMu[n]^2*n^(power)/(n - EulerPhi[n]), {n, 2, nn}]]
 (*Mathematica end*)