  In this paper based on a sort of linear function, a deterministic and simple
algorithm with an algebraic structure is presented for calculating all (and
only) $k$-almost primes ($where$ $\exists n\in {\rm N} $, $1{\le} k {\le}n$) in
certain interval. A theorem has been proven showing a new deterministic
property of the category of $k$-almost primes. Through a linear function that
we obtain, an equivalent redefinition of the $k$-almost primes with an
algebraic characteristic is identified. Moreover, as an outcome of our
function's property some relations which contain new information about the
$k$-almost primes (including primes) are presented.
