  In this article, we prove that for a completely multiplicative function $f$
from $\mathbb{N}^*$ to a field $K$ such that the set $$\{p \;|\; f(p)\neq 1_K
\;\mbox{and }p \mbox{ is prime}\}$$ is finite, the asymptotic subword
complexity of $f$ is $\Theta(n^t)$, where $t$ is the number of primes $p$ that
$f(p)\neq 0_K, 1_K$. This proves in particular that sequences like
$((-1)^{v_2(n)+v_3(n)})_n$ are not $k$-automatic for $k\geq 2$.
