How do I plot a 2d curve and label lattice points to one side of it?

I want to plot the curve $f[x]=\frac{1}{x}$, and draw a solid red dot at every lattice point in the following set: $$\{(m,n)\in \mathbb N^2\colon mn\geq 1\}$$

  • $\begingroup$ Make a lattice with Tuples, filter it with Select, plot with ListPlot, combine it with the curve using Show. $\endgroup$ – Szabolcs Jul 23 '15 at 6:37
  • $\begingroup$ You can add something like Epilog -> {Red, Point[Flatten[Array[List, {5, 5}], 1]]} to your plot. $\endgroup$ – J. M.'s discontentment Jul 23 '15 at 6:41

In V10.1 or later, you can use CoordinateBoundingBoxArray to generate the lattice.

With[{m = 5},
  Plot[1/x, {x, 0, m},
    Epilog -> {
      Red, PointSize[Medium],
      Point[Flatten[CoordinateBoundingBoxArray[{{1, 1}, {m, m}}], 1]]},
    AspectRatio -> Automatic,
    PlotRange -> {0, m},
    PlotRangePadding -> .15,
    Frame -> True]]


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