  In this paper we study some structure properties of primitive weird numbers
in terms of their factorization. We give sufficient conditions to ensure that a
positive integer is weird. Two algorithms for generating weird numbers having a
given number of distinct prime factors are presented. These algorithms yield
primitive weird numbers of the form $mp_1\dots p_k$ for a suitable deficient
positive integer $m$ and primes $p_1,\dots,p_k$ and generalize a recent
technique developed for generating primitive weird numbers of the form
$2^np_1p_2$. The same techniques can be used to search for odd weird numbers,
whose existence is still an open question.
