Palindromicity means negated reversals of sequence in column

"Palindromicity means negated reversals of sequences in columns:"

(*start*)
(*Mathematica*)
Clear[a, n, k, m, nn];
nn = 12;
a[n_] := Total[MoebiusMu[Divisors[n]]*Divisors[n]];
TableForm[
 Table[Table[
   If[n <= k, Sum[a[GCD[m, k]], {m, 1, n}], ""], {k, 1, nn}], {n, 1,
   nn}]]
TableForm[
 Table[Table[
   If[And[n >= k - 1, n <= 2*k - 2], Sum[a[GCD[m, k]], {m, k, n}],
    ""], {k, 1, nn}], {n, 1, 2*nn}]]
(*end*)