Let An={x∈N:gcd(x,n!)=1}A_n = \{x \in \mathbb{N} : \text{gcd}(x, n!) = 1\}An={x∈N:gcd(x,n!)=1} for n∈Nn \in \mathbb{N}n∈N (natural numbers, starting from 1). Determine the set S=⋂n=1∞AnS = \bigcap_{n=1}^{\infty} A_nS=⋂n=1∞An.
∅\emptyset∅
{1}\{1\}{1}
The set of all prime numbers
N\mathbb{N}N