Determine whether each of these sets is countable or uncountable. For those that are countably infinite, exhibit a one-to-one correspondence between the set of positive integers and that set.
1) Integers not divisible by $3$.
2) Integers divisible by $5$ but not by $7$.
I figured out the first one so it was $3k+1$ or $3k+2$ but the second one has thrown me for a loop I was thinking it could be something like $5k$ but that will give me everything divisible by $5$ and $7$, can't figure out what to do about the not divisible by $7$.
Both are countable since I could go though and count the numbers that meet the requirements or am I wrong?