I am interested in finding out the name of the following polynomials (if already named) and additionaly any of their properties:
$$p_N(x) = \sum_{d|N}{x^{d+\frac{N}{d}}}$$
It is clear they will only have +2 values as coefficients and exceptionally a +1 one when N is a perfect square. I also guessed they would be related to cyclotomic polynomial as their definition involve a Dirichlet convolution too, but no clear at all in which way it could be.
Thanks in advance.