von Mangoldt function and Riemann zeta zeros

Mathematica


Clear[A, B, n, k, T, nn]
nn = 24;

A = Table[Table[N[Re[k^ZetaZero[n]], 12], {k, 1, nn}], {n, 1, nn}];

MatrixForm[A]
T[n_, k_] :=
T[n, k] =
If[n < 1 || k n, T[k, n],
If[n > k, T[k, Mod[n, k, 1]], -Sum[T[n, i], {i, n - 1}]]]]];

B = Table[Table[T[n, k]/n, {k, 1, nn}], {n, 1, nn}];

MatrixForm[B]
Total[A]
Total[N[B, 10]]

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