Clear[nn, k, n, a, res];

res = 100;

Monitor[a =

N[Table[Sum[

MangoldtLambda[n]*1/n*

Sum[Cos[-nn*(k - 1)/n*2*Pi], {k, 1, n}], {n, 1, nn}], {nn, 1,

res, 1/res}]];, N[nn]]

g1 = ListLinePlot[a, DataRange -> {1, res}];

Show[g1, ImageSize -> Full]

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