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They seem like a good source of programming problems.
Before 2003, they were stupidly hard puzzler in algorithm design. 2003 to 2006 were utterly pedestrian exercise in typing a lot of lines of code. I just glanced at 2007 and beyond, and they look better. They are of the form: here's some tricky math for an algorithm, go implement it. I like that better.
Instead of some-divides? , I would do

(require (rename-in srfi/26 [cut //]))(ormap (// divide? <> div) nums)
I wanted to use for/or and the other for/X constructs because it lets me play with the generalized iteration support. Lists are so passe. :)

For example, I've changed the function recently to walk across a vector rather than a list. ormap wouldn't let me do that so easily as it constrains the thing I'm iterating across to lists.
Yeah, Racket's collections are such a mess compared to Clojure's.