Are there names for any of these four classes of numbers related to divisors and totatives?
- A [insert name here] of $n$ is a positive integer $\leq n$ that isn't a divisor of $n$ and that can be multiplied by some other integer to produce a power of $n$.
- A [insert name here] of $n$ is a positive integer $\leq n$ that can be multiplied by some other integer to produce a power of $n$. (This class of numbers is composed of the previous class of numbers plus the divisors.)
- A [insert name here] of $n$ is a positive integer $\leq n$ that is the product of at least one prime divisor of $n$ and at least one prime totative of $n$.
- A [insert name here] of $n$ is a positive integer $\leq n$ that is either a totative of $n$ or the product of at least one prime divisor of $n$ and at least one prime totative of $n$. (This class of numbers is composed of the previous class of numbers plus the totatives.)
For example, for $n=18$ here are all the numbers in all the four classes:
- {4, 8, 12, 16}
- {1, 2, 3, 4, 6, 8, 9, 12, 16, 18}
- {10, 14, 15}
- {5, 7, 10, 11, 13, 14, 15, 17}
I've done some research, and I found two articles about two classes of numbers that are somewhat similar to class number 2:
- The class of regular numbers according to Wikipedia is like class number 2, except that this class is restricted to $n=30k$ (because they are used in the study of the Babylonian's sexagesimal numeral system ) and the numbers are not restricted to being $\leq n$.
- The class of regular numbers according to Wolfram MathWorld is like class number 2, except that this class is restricted to $n=10k$ (because they are used in the study of our decimal numeral system) and the numbers are not restricted to being $\leq n$.
OEIS tells me that 1. is the set of semidivisors (https://oeis.org/A243822), 2. is the set of semidivisors or divosors (naturally) and has no idea, how could be 3. and 4. named. I have assumed in my reasearch that you are only interested in products of two primes, if that is not the case please correct me.