  Let $A$ be a set of positive integers. We define a positive integer $n$ as an
$A$-practical number if every positive integer from the set $\left\{1,\ldots
,\sum_{d\in A, d\mid n}d\right\}$ can be written as a sum of distinct divisors
of $n$ that belong to $A$. Denote the set of $A$-practical numbers as
$\text{Pr}(A)$. The aim of the paper is to explore the properties of the sets
$\text{Pr}(A)$ (the form of the elements, cardinality) as $A$ varies over the
power set of $\mathbb{N}$. We are also interested in the set-theoretic and
dynamic properties of the mapping $\mathcal{PR}:\mathcal{P}(\mathbb{N})\ni
A\mapsto\text{Pr}(A)\in\mathcal{P}(\mathbb{N})$.
