In arithmetic, there are common terms such as rational numbers, irrational numbers, whole numbers, natural numbers etc. Here are some less known numbers:
1) Evil numbers: Numbers with a binary representation with even number of 1s. An example of an evil number is pi
3) Unhappy numbers, ie numbers which are not happy.
4) Wasteful numbers: If x is a wasteful number, its prime factorisation has more digits (including the powers)than the number of digits of x. An example is 4,6,8,9,12,18 etc.
5) Frugal numbers: A non wasteful number and 1.
6) Economic numbers: Frugal numbers excluding 1.
7) I like this one the most: Lucky numbers
There are many other types of numbers. Here's a nice article on number gossip.