Knödel number

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 $i^{m-n}\equiv 1(\mathrm{mod}m)$. The concept is named after Walter Knödel.Template:Citation needed

The set of all n-Knödel numbers is denoted K_n. 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 $n=m-\phi (m)$ where $\phi$ is Euler's totient function.

Examples

n	Kn
1	{561, 1105, 1729, 2465, 2821, 6601, ... }	Template:OEIS
2	{4, 6, 8, 10, 12, 14, 22, 24, 26, ... }	Template:OEIS
3	{9, 15, 21, 33, 39, 51, 57, 63, 69, ... }	Template:OEIS
4	{6, 8, 12, 16, 20, 24, 28, 40, 44, ... }	Template:OEIS

Literature

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Template:Classes of natural numbers

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