# note on quotients of lacunary functions

Define:

$\lambda_{a}(q) \equiv 1 + \sum_{n=1}^{\infty} q^{a^{n}}$ and

$\l_{a}(q) \equiv 1 + \sum_{n=1}^{\infty} (-1)^{n} q^{a^{n}}$

Preliminary numerical experiments suggest that the power series representations of their quotients $l_{b}(q)/\lambda_{a}(q)$ and $\lambda_{a}(q)/l_{b}(q)$ always have integer coefficients.