Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
a(1)=1, a(p)=p if p is a prime. Otherwise, start with n and iterate the map (k -> concatenation of proper divisors of k) until we reach a prime q; then a(n) = q. If we never reach a prime, a(n) = -1.
8 -> 2.4 -> 24 -> 2.3.4.6.8.12 -> 2346812 -> 2.4.13.26.52.45131.90262.180524.586703.1173406 -> 2413265245131902621805245867031173406 -> ? (see link for the continuation)