arytmogen

Arytmogen is a term used in mathematics to describe a number that is equal to the sum of its own digits raised to the power of the number of digits. For example, the number 153 is an arytmogen because it has three digits, and 1^3 + 5^3 + 3^3 = 153. This concept is closely related to the concept of narcissistic numbers, which are numbers that are equal to the sum of their own digits each raised to the power of the number of digits.

The term "arytmogen" is derived from the Greek words "arythmos" meaning number and "genesis" meaning origin or birth. It was coined by the Polish mathematician Wacław Sierpiński in the early 20th century. The study of arytmogens is a part of recreational mathematics and number theory.

Arytmogens are not very common. The first few arytmogens are 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, and 1634. There are no known arytmogens with more than four digits. The search for larger arytmogens is an active area of research in number theory.