  Bloch-Okounkov studied certain functions on partitions $f$ called shifted
symmetric polynomials. They showed that certain $q$-series arising from these
functions (the so-called \emph{$q$-brackets} $\left<f\right>_q$) are
quasimodular forms. We revisit a family of such functions, denoted $Q_k$, and
study the $p$-adic properties of their $q$-brackets. To do this, we define
regularized versions $Q_k^{(p)}$ for primes $p.$ We also use Jacobi forms to
show that the $\left<Q_k^{(p)}\right>_q$ are quasimodular and find explicit
expressions for them in terms of the $\left<Q_k\right>_q$.
