This is the latest inwards book, a three volume histoy of theory of numbers.

Vol 1 has a whole chapter (IV) on sevenites, under the title of the form of Euler's Quotient, p 105-112. Weiferich is mention in passing, but the original question was raised by Abel in 1828, and answered by examples by Jacobi (1839), the decimal sevenites 3 and 487 at least by 1852 (Desmarest).

Neither Dickson nor David Wells (1975) seemed to have a general name.

It's prettty encrusted in mathematica runes, so this is not an easy read, and i suppose it's down to looking at the pretty pictures.

Now what you called "sevenites" are called "base b Wieferich primes" or "generalized Wieferich primes" *today* by a significant contingent of international mathematicians, texts notwithstanding. I have Oystein Ore's history of the theory of numbers wherein he talks of "aliquot parts" meaning proper divisors. This is old diction that few use today; I read other mathematicians in later works fondly recalling Ore's "quaint writing" with terms like "aliquot part" that aren't used today.

What was the title of the chapter? It wasn't "Sevenites", was it?

Dan had a concept we called "abstract prime factorization" that a significant contingent of international mathematicians call "prime signature." Now we call it "prime signature" too, because that enables others to better understand what we're talking about.

I didn't mind using "sevenite" when there didn't seem to be a canonical term for such a thing, though it never sat well. The Russians have a word "vokzal" meaning train station. It was a long time that I came to understand that this word is taken from the name of an actual train station - Vaux Hall. What's so special about Vaux Hall (I'm sure it's pretty). My Greek friend is of course bent against Turks. He says that the conquerors of Constantinople got there by asking "where's the city," and kept getting the reply ending in "to the city" thus that is how he says Istanbul got it's name (I don't think it's true. I think it's K(i)n(stan)tino(bul)is = Istanbul. Happens all the time. Look what they did to Cordoba <= Al Qartuba <= Kar-Juba. When we take over a foreign city we can't seem to pronounce it right). So in his mind Constantinople was renamed "To the city". The Italian word in common use for a bus is pullman, from an actual make. Sevenite is a similar term. I'd rather not have a general term from a specific instance (apparently 7 in base 18.)

I don't like "generalized Wieferich prime" because it is ten years long and I am not sure how to say "Wieferich" (then again my surname is a doozie, so you won't see any eponymous functions or discoveries from me, thank you). But it is what that is called and I think we should use it if we want to be understood.

Mathematica function for finding base-b Wieferich primes:

f[b_, lim_] := Select[Prime@ Range@ lim, Divisible[b^(# - 1) - 1, #^2] &]

Implementation for base 18:

f[18, 18^3]

Output:

{5, 7, 37, 331, 33923}

By this, it might've been called "fivites" just as easily ; ).