For Lucas sequences of the first kind and second kind defined as usual by , , where and are either integers or conjugate quadratic integers, we describe the sets     divides  and     divides . Building on earlier work, particularly that of Somer, we show that the numbers in these sets can be written as a product of a so-called basic number, which can only be , or , and particular primes, which are described explicitly. Some properties of the set of all primes that arise in this way is also given, for each kind of sequence.