Could be Euler product for Riemann zeta function runs over pseudo-prime?

Question

The Euler product over primes defined as :$$\zeta(s)=\prod_{p \ \text{prime}} \frac{1}{1-p^{-s}}\tag{01}$$ , My question Here is : is it possible to write this product $(01)$ for which run or extends over pseudoprime in any context of it's mathematical definition ( For example Fermat pseudo-prime)

Answer 1

No, because the product depends on prime factorization and so has to use the actual primes.