On williams numbers with three prime factors

Let a Є ℤ\ {0}. A positive squarefree integer N is said to be an a-Korselt number (K _a -number, for short) if N ≠ a and p−a divides N −a for each prime divisor p of N. By an a-Williams number (W _a -number, for short) we mean a positive integer which is both an a-Korselt number and (−a)-Korselt number. This paper proves that for each a there are only finitely many W _a - numbers with exactly three prime factors, as conjectured in 2010 by Bouallegue-Echi-Pinch.