  We introduce a variation on the prime divisor function $B(n)$ of Alladi and
Erd\H{o}s, a close relative of the sum of proper divisors function $s(n)$.
After proving some basic properties regarding these functions, we study the
dynamics of its iterates and discover behaviour that is reminiscent of aliquot
sequences. We prove that no unbounded sequences occur, analogous to the
Catalan-Dickson conjecture, and give evidence towards the analogue of the
Erd\H{o}s-Granville-Pomerance-Spiro conjecture on the pre-image of $s(n)$.
