What is a mangle number?

A mangle number is a term used in mathematics to describe a number that can be expressed as the sum of the digits of its own factorial. For example, 1 and 2 are considered mangle numbers because (1! = 1) and (2! = 2), and the sum of their digits equals the numbers themselves. However, as numbers increase, finding mangle numbers becomes increasingly rare. The concept is part of recreational mathematics and explores interesting properties of numbers.