  We provide a uniform bound on the partial sums of multiplicative functions
under very general hypotheses. As an application, we give a nearly optimal
estimate for the count of $n \le x$ for which the Alladi-Erd\H{o}s function
$A(n) = \sum_{p^k \parallel n} k p$ takes values in a given residue class
modulo $q$, where $q$ varies uniformly up to a fixed power of $\log x$. We
establish a similar result for the equidistribution of the Euler totient
function $\phi(n)$ among the coprime residues to the "correct" moduli $q$ that
vary uniformly in a similar range, and also quantify the failure of
equidistribution of the values of $\phi(n)$ among the coprime residue classes
to the "incorrect" moduli.
