period lengths in summatory von Mangoldt function matrix

(*start*)
Clear[a, b, f, p];
nn = 600;
f[n_] := n;
a[n_] := DivisorSum[n, MoebiusMu[#] # &];
Monitor[TableForm[
   A = Accumulate[
     Table[Table[a[GCD[n, k]], {k, 1, nn}], {n, 1, nn}]]];, n]
Table[
 n = row;
 first = Table[Table[A[[n, k]], {k, 1, kk}], {kk, 1, nn/2}];
 further = Table[Table[A[[n, k]], {k, kk + 1, 2*kk}], {kk, 1, nn/2}];
 differences = first - further;
 numberOfZeros =
  Table[n - Count[differences[[n]], 0], {n, 1, Length[differences]}];
 First[Flatten[Position[numberOfZeros, 0]]], {row, 1, 10}]
(*end*)

 {1, 2, 6, 6, 30, 30, 210, 210, 210, 210}
which apparently are the primorial numbers.

(*start*)
Clear[a, b, f, p];
nn = 600;
f[n_] := n;
a[n_] := DivisorSum[n, MoebiusMu[#] # &];
Monitor[TableForm[
   A = Accumulate[
     Table[Table[a[GCD[n, k]], {k, 1, nn}], {n, 1, nn}]]];, n]
A = Transpose[A];
Table[
 n = row;
 first = Table[Table[A[[n, k]], {k, 1, kk}], {kk, 1, nn/2}];
 further = Table[Table[A[[n, k]], {k, kk + 1, 2*kk}], {kk, 1, nn/2}];
 differences = first - further;
 numberOfZeros =
  Table[n - Count[differences[[n]], 0], {n, 1, Length[differences]}];
 First[Flatten[Position[numberOfZeros, 0]]], {row, 2, 70}]
(*end*)

Period lengths of columns are not found in the OEIS:
{2, 3, 2, 5, 6, 7, 2, 3, 2, 11, 6, 13, 2, 15, 2, 17, 6, 19, 2, 3, 2, \
23, 6, 5, 2, 3, 2, 29, 30, 31, 2, 3, 2, 35, 6, 37, 2, 3, 2, 41, 42, \
43, 2, 15, 2, 47, 6, 7, 2, 3, 2, 53, 6, 5, 2, 3, 2, 59, 30, 61, 2, 3, \
2, 5, 66, 67, 2, 3, 2}
Although there is a near match but it begins to differ at n=42.