  We prove a central limit theorem for the joint distribution of $s_q(A_jn)$,
$1\le j \le d$, where $s_q$ denotes the sum-of-digits function in base~$q$ and
the $A_j$'s are positive integers relatively prime to $q$. We do this in fact
within the framework of quasi-additive functions. As application, we show that
most elements of "Catalan-like" sequences - by which we mean integer sequences
defined by products/quotients of factorials - are divisible by any given
positive integer.
