Question: Plot of Harmonic Numbers

I'm trying to reproduce the following graph:

http://upload.wikimedia.org/wikipedia/commons/thumb/2/22/HarmonicNumbers.svg/600px-HarmonicNumbers.svg.png

I have got this far:

N:=10:
theHarmonicNumbersPlot := plot([seq([n,sum(1/i,i=1..n-1)-gamma],n=2..N)],style=point, colour=red):
theHarmonicFunctionPlot := plot(Psi(n), n=2..N, colour=black):
plots:-display([theHarmonicFunctionPlot,theHarmonicNumbersPlot]);

But my plot is missing the horizontal unit-segments that I think would look nice.

Thanks for any suggestion,

Patrick.

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