[seqfan] The Mangoldt function as convergents of Dirichlet series.

[Mats Granvik]

This appears to be the Mangoldt function as convergents of Dirichlet series.
It takes a while to converge.

Mathematica program:

Clear[t, n, k, a, b, c, d, M, EM];
nn = 5000;
mm = 100;
t[n_, 1] = 1;
t[1, k_] = 1;
t[n_, k_] :=
   t[n, k] =
    If[n < k,
     If[And[n > 1, k > 1], Sum[-t[k - i, n], {i, 1, n - 1}], 0],
     If[And[n > 1, k > 1], Sum[-t[n - i, k], {i, 1, k - 1}], 0]];
a = Table[Table[t[n, k], {k, 1, mm}], {n, 1, nn}];
b = Range[1, nn];
c = a/b;
MatrixForm[c];
d = N[Table[Total[c[[All, i]]], {i, 1, mm}]]
M = Exp[d]
EM = Round[Exp[d]]


DI Mats Granvik
Tel: +358 50 570 8324
CV: http://matsgranvik.wordpress.com/