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 .[1] The concept is named after Walter Knödel.
The set of all n-Knödel numbers is denoted Kn.[1] The special case K1 is the Carmichael numbers.[1] 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.
Examples
| n | Kn | |
|---|---|---|
| 1 | {561, 1105, 1729, 2465, 2821, 6601, ... } | (sequence A002997 in the OEIS) |
| 2 | {4, 6, 8, 10, 12, 14, 22, 24, 26, ... } | (sequence A050990 in the OEIS) |
| 3 | {9, 15, 21, 33, 39, 51, 57, 63, 69, ... } | (sequence A033553 in the OEIS) |
| 4 | {6, 8, 12, 16, 20, 24, 28, 40, 44, ... } | (sequence A050992 in the OEIS) |
References
- 1 2 3 Weisstein, Eric W. "Knödel Numbers". mathworld.wolfram.com. Retrieved 2021-09-14.
Literature
- Makowski, A (1963). Generalization of Morrow's D-Numbers. p. 71.
- Ribenboim, Paulo (1989). The New Book of Prime Number Records. New York: Springer-Verlag. p. 101. ISBN 978-0-387-94457-9.
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