Try en.wikipedia.org/wiki/Divisor_function for the basics on the function d(n).

Perhaps you have a mental picture of orthogonal projection, when the projection is not always orthogonal?

The problem seems a bit more subtle than I originally gave it credit for. You may need more than just equidistribution.

I didn't express an opinion on the answer.

@alvarezpaiva Actually this is uncalled-for. One of my undergraduate students went on to do Ph.D. work at Oxford on Higgs bundles. In those days I did work at understanding the mathematics, but it was quite some time ago. I said geometrical theories in that sense.

I have clarified that I'm concerned to ask about Higgs bundles.