How many integers are there that are not divisible by any prime larger than 20 and not divisible by the square of any prime?

Question

I tackled the problem in the following way but i'm not sure if i'm correct.

I need the count of the numbers that have in their prime factorization only primes p such that $p \lt 20$ and those numbers can't be more than once in the prime factorization (right?)

So, the amount of numbers that can be expressed this way are all the subsets of the set $\{2,3,5,7,11,13,17,19\} = 2^8$.

Correct me if I'm wrong.

Answer 1

Your method is perfectly correct, but if it is actually about integers then you need to include negatives as well to have twice as many.

I suspect this is not the case however since then if you said "primes $p<20$" you'd probably have to include negative primes as well, in which case there would be infinitely many.