It also is very very clearly one of the inspirations for Douglas Adams' Hitch-Hiker's Guide. I think Adams, as an sf fan, would have appreciated this but also been somewhat disappointed, and the Encyclopedia Galactica (itself of course referenced by Adams) is an obvious source - providing framing description, introduced by its own little twiddle, words spoken by an actor who is otherwise separate from the action. Adams' genius was to take this model and subvert it so memorably. This audio version of the Foundation trilogy, rather more than the original books, is a crucial seed text for Arthur Dent and Zaphod Beeblebrox.
Thanks to james_nicoll for pointing it out in the first place.