Andrews and Sellers recently initiated the study of arithmetic properties of
Fishburn numbers. In this paper, we prove prime power congruences for
generalized Fishburn numbers. These numbers are the coefficients in the $1-q$
expansion of the Kontsevich-Zagier series $\mathscr{F}_{t}(q)$ for the torus
knots $T(3,2^t)$, $t \geq 2$. The proof uses a strong divisibility result of
Ahlgren, Kim and Lovejoy and a new "strange identity" for $\mathscr{F}_{t}(q)$.