  We investigate strong divisibility sequences and produce lower and upper
bounds for the density of integers in the sequence which only have (somewhat)
large prime factors. We focus on the special cases of Fibonacci numbers and
elliptic divisibility sequences, discussing the limitations of our methods. At
the end of the paper there is an appendix by Sandro Bettin on divisor closed
sets, that we use to study the density of prime terms that appear in strong
divisibility sequences.
