For Lucas sequences of the first kind (u_n) and second kind (v_n) defined as
usual for positive n by u_n=(a^n-b^n)/(a-b), v_n=a^n+b^n, where a and b are
either integers or conjugate quadratic integers, we describe the set of indices
n for which n divides u_n and also the set of indices n for which n divides
v_n. 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 1, 6 or 12, 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
