> Obviously, it's fairly easy to get a 1300 Hz square wave, but
> what can I do to simply and easily smooth this out a bit, so it's
> reasonably close to a sine wave?

Try a triangular wave and a little external RC smoothing. The topic
has come up before, it should be in the archives

Or this will convert a triangle to a pretty good sine wave

http://home.clear.net.nz/pages/joecolquitt/tri2sine.html

Obviously not optimised for a single 5V supply though, but that
shouldn't be too difficult. I've made this many times, but always
for signals that needed to be centered around 0V, not mid-rail

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