von Mangoldt function from Dirichlet Characters

(*Mathematica program start*)
nn = 42;
b = Table[
   Exp[MangoldtLambda[Divisors[n]]]^-MoebiusMu[Divisors[n]], {n, 1,
    nn}];
j = 1;
A = Table[
   Table[Product[(b[[n]][[m]]*
        DirichletCharacter[b[[n]][[m]], j, k] - (b[[n]][[m]] -
         1)), {m, 1, Length[Divisors[n]]}], {n, 1, nn}], {k, 1, nn}];
vonMangoldtFunction =
 N[Table[Sum[A[[n, k]]/k, {k, 1, nn}], {n, 1, nn}]]
ListLinePlot[vonMangoldtFunction]
(*Mathematica program end*)