In this article, we prove that for a completely multiplicative function f from N * to a field K such that the set {p | f (p) = 1K and p is prime} is finite, the asymptotic subword complexity of f is Θ(n t ), where t is the number of primes p that f (p) = 0K , 1K . This proves in particular that sequences like ((−1) v 2 (n)+v 3 (n) )n are not k-automatic for k ≥ 2.