What is the totient function for an RSA modulus has several factors due to incorrect setup? $ϕ(n)=p.q−(p+q)+1$ where there are two factor $p$ and $q$, but what if there were 3 (or more) factors such as $(p,q,r)$ due to a typo in specifying the modulus?
$\phi(p \cdot q \cdot r \cdot ... \cdot s) = (p-1)(q-1)(r-1)...(s-1)$ (for $p, q, r, ..., s$ distinct primes)

In addition, the technically correct modulus for which $e \cdot d \equiv 1$ must hold is commonly known as $\lambda(n)$; in this case,

$\lambda(p \cdot q \cdot r \cdot ... \cdot s) = \text{lcm}(p-1, q-1, r-1, ..., s-1)$