How to notate all integers $\gt 1$ except products of $2, 3 , 5$?

Question

What is a notation for all whole numbers greater than $6$ which are not a product of $2, 3 , 5$? $7$ would the first, then $11, 13, \ldots$ also $7\times 7$ or $11\times 11$ would be included.

As a clarification, start of the sequence would be:

$$7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 77, 79, 83, 89, 91, 97, 101,\ldots$$

Answer 1

These are the positive integers that are not 5-smooth. These numbers are also called 7-rough. Alternatively, if you want a set notation, $$S = \{n \in \mathbb N_{>1}: 2 \nmid n, 3 \nmid n, 5 \nmid n\}$$

works.

Answer 2

You could use $(\mathbb{N}+6) \setminus (2\mathbb{Z} \cup 3\mathbb{Z} \cup 5\mathbb{Z})$.

Answer 3

The other answers are correct, but here is an attempt at a compact approach: $$\{n\in\mathbb{N}_{>1}:\gcd(n,30)=1\}$$

Answer 4

The following also works :

$$\{n\mid n\in\mathbb N,n\not=1,n^2\equiv 1,19\pmod{30}\}$$