@Kitonum This is definitely a good idea, if only a little bit complicated for a Maple newbie. But thanks to you I can now try it that way.

However, the original problem was not that " Maple connects consecutive points with line segments" but that Maple omits (72,4) and hence connects nonconsecutive points.

Meanwhile I found that this can be remedied by telling Maple to use 1000 points when plotting:

Notice that the missing point is inserted now.

@tomleslie I am not quite sure what you mean by "integerize", since the original function has integer values already.

Furthermore, your new function seems not to coincide with it, as can be seen here:

diff := n->ceil(sqrt(4*floor(n)))-floor(sqrt(2*floor(n)))-1-(ceil(sqrt(4 n))-floor(sqrt(2 n))-1); plot(diff, 10 .. 100, gridlines = false)