Edit 14.10.2012: Unfortunately copy pasting into wordpress makes the code show wrong, and it will not work.

Mathematica 8

aa = 32;

a = Range[aa]*0;

Monitor[Do[

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}]]]]];

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

A[[1, All]] = 0;

a[[nn]] = Total[Total[A]], {nn, 1, aa}], nn]

b = a;

c = Accumulate[Table[N[MangoldtLambda[n]], {n, 1, aa}]];

g2 = ListPlot[{c, b}, ImageSize -> Full]

Link to Pastebin with working code:

von Mangoldt function and von Mangoldt matrix

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