The $9_{46}$ odd-index $F$-factor divisibility conjecture

Let $9_{46}$ be the pretzel knot $(3,3,-3)$, and let $F_i$ denote its $i$th $F$-factor. For each positive integer $i$, the relevant divisor is $1+A^2q^{2(i-1)}$.

The $9_{46}$ odd-index divisibility conjecture. For odd positive integers $i>1$,

$$(1+A^2q^{2(i-1)})\mid F_i.$$

The stated factorization is observed for $F_1$, $F_3$, $F_5$, and $F_7$, but the general assertion is unproved.