Knödel number
Encyclopedia
A 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 set of all such integer
s for n is then called the set of Knödel numbers Kn.
The special case K1 are the Carmichael numbers.
Composite number
A composite number is a positive integer which has a positive divisor other than one or itself. In other words a composite number is any positive integer greater than one that is not a prime number....
m with the property that each i < m coprime
Coprime
In number theory, a branch of mathematics, two integers a and b are said to be coprime or relatively prime if the only positive integer that evenly divides both of them is 1. This is the same thing as their greatest common divisor being 1...
to m satisfies
. The set of all such integerInteger
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
s for n is then called the set of Knödel numbers Kn.
The special case K1 are the Carmichael numbers.
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, ... } |