Is the following function reducible in any way, even if just for simplifying the computation of it at a single point (e.g. with Taylor series expansion)? I'm also curious if anyone has seen or studied this particular function (or variants of it) before. Does it have a name, for example?
$$ p(x) = -\sin(2\pi x) \sum_{n=2}^\infty \frac{\tan(\pi x/n+\pi/2)}{2n} $$
The function appears to have a value of 1 with a slope of 0 at the primes.
