I just encountered the prime number wiki and when looking through some of them, or even regular numbers, you see dozens of new terms you never encounter in other areas of math such as:
- centered pentagonal number
- nontotient
- Harshad number
- sphenic number
- balanced prime
- sexy prime
- happy number
- ... phew
I have looked through a bit of the different areas of math but I haven't ever seen stuff like this with all these names for different numbers and the features of individual numbers. I assume this all is covered in Number Theory, but I'm just not sure what the best place is to look it up quickly and thoroughly.
I would like to know if there is a book or anything (preferably something freely available online) other than Wikipedia that goes through all of the different possible number theory terms (or as many as possible to be thorough), and perhaps any theorems/lemmas/proofs if that's the style. I like the books that are concise and just pure Lemma/Theorem/Definition -> Lemma/Theorem/Definition -> Lemma/Theorem/Definition ... no fluff, if at all possible.
Mathworld
Prime pages
OEIS
Numberphile
standupmaths
singingbanana
Mathologer
Come to mind. Numberphile has videos on sets, sexy primes, and happy numbers. If you don't have some elementary set theory knowledge, number theory will be basically impossible.
EDIT Also forgot List of Mathematical symbols,List of math jargon,Glossary of math etc.