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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)