definition of anti-divisor

[Max Alekseyev]

On 7/21/07, N. J. A. Sloane <njas at research.att.com> wrote:

> Definition: If an odd number i in the range 1 < i <= n divides N
> where N is any one of 2n-1, 2n or 2n+1
> then d = N/i is called an anti-divisor of n.
>
> Equivalently, an anti-divisor of n is a number d in the range [1..n]
> which does not divide n and is either an odd divisor of 2n-1 or 2n+1,
> or an even divisor of 2n.

Yet another definition:

k is a non-divisor of n iff:
1 < k < n
and
| (n mod k) - k/2 | <= 1.

Max