Leyland number

In number theory, a Leyland number is a number of the form

where x and y are integers greater than 1. They are named after the mathematician Paul Leyland. The first few Leyland numbers are

The requirement that x and y both be greater than 1 is important, since without it every positive integer would be a Leyland number of the form x + 1. Also, because of the commutative property of addition, the condition x ≥ y is usually added to avoid double-covering the set of Leyland numbers (so we have 1 < y ≤ x).