  In a recent paper, Bruinier and Ono prove that the coefficients of certain
weight -1/2 harmonic Maass forms are traces of singular moduli for weak Maass
forms. In particular, for the partition function $p(n)$, they prove that
\[p(n)=\frac{1}{24n-1} \sum P(\alpha_Q),\] where $P$ is a weak Maass form and
$\alpha_Q$ ranges over a finite set of discriminant $-24n+1$ CM points.
Moreover, they show that $6 (24n-1) P(\alpha_Q)$ is always an algebraic
integer, and they conjecture that $(24n-1) P(\alpha_Q)$ is always an algebraic
integer. Here we prove a general theorem which implies this conjecture as a
corollary.
