In number theory, an n-Knödel number for a given positive integer n is a composite number m with the property that each i < m coprime to m satisfies . The concept is named after Walter Knödel.
The set of all n-Knödel numbers is denoted Kn. The special case K1 is the Carmichael numbers. There are infinitely many n-Knödel numbers for a given n.
Due to Euler's theorem every composite number m is an n-Knödel number for where is Euler's totient function.
A 1-Knödel number is commonly known as a Carmichael number, and a 3-Knödel number is also known as a D-number.
Examples
n Kn 1 {561, 1105, 1729, 2465, 2821, 6601, ... } 2 {4, 6, 8, 10, 12, 14, 22, 24, 26, ... } 3 {9, 15, 21, 33, 39, 51, 57, 63, 69, ... } 4 {6, 8, 12, 16, 20, 24, 28, 40, 44, ... }
References
Literature