definition of anti-divisor

[Max Alekseyev]

Except element 4, the elements of A066466 have form 2^k*p where p is
odd prime and both 2^(k+1)*p-1, 2^(k+1)*p+1 are prime (i.e., twin
primes).
In other words, A066466 without element 4 is a subsequence of A040040,
containing elements of the form 2^k*p with prime p.

Max

On 7/23/07, Jonathan Post <jvospost3 at gmail.com> wrote:
> Any work since 2001 on whether or not there is a 6th anti-prime?  How
> far has this been searched?  Any proofs or disproofs as to finiteness
> of A066466?
>
> COMMENT FROM Jonathan Vos Post RE A066466
>
> %I A066466
> %S A066466 3, 4, 6, 96, 393216
> %N A066466 Numbers having just one anti-divisor.
> %C A066466 Jon Perry calls these anti-prime numbers, saying that these
> are the only 5 known. This sequence is worth extending, if possible,
> or proving finite.
> %F A066466 A066272(a(n)) = 1.
> %Y A066466 Cf. A066272.
> %O A066466 1
> %K A066466 ,more,nonn,
> %A A066466 Jonathan Vos Post (jvospost2 at yahoo.com), Jul 23 2007
>