Leyland number

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

${\displaystyle x^{y}+y^{x}}$

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

8, 17, 32, 54, 57, 100, 145, 177, 320, 368, 512, 593, 945, 1124 (sequence A076980 in the OEIS).

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 x¹ + 1^x. 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).