Am I right to be surprised by this big clump of numbers divisible by large squares within a not-so-long interval? If so, should I be surprised because $(1)$ this rarely happens, or because $(2)$ it's something I didn't know about and couldn't have seen coming? Should $19^2\times205$ be given litt...

For graphs $F$ and $G$, let $\hom(F,G)$ denote the number of homomorphisms (adjacency preserving maps) from $F$ to $G$. Define a relation $\le_{\hom}$ on (isomorphism classes of) graphs as $G \le_{\hom} H$ if $\hom(F,G) \le \hom(F,H)$ for all graphs $F$. This relation is clearly reflexive and tra...