Concatenated anti-divisors

[Maximilian Hasler]

It first appeared as if "your" definition (the second below) could be
found at least on some other web pages. Now I have big doubts. Is
there any *serious* reference for this notion ?
According to "your" definition,
antidiv( 3 ) = { 2, 5, 6, 7 }
since none of these numbers divide 3 and they are either even divisors
of 6 or odd divisors of 5 or 7.

Also, concerning the sequence :

A130799 Triangle read by rows in which row n (n>=3) list the anti-divisors of n.

I cannot see any triangular structure (cf.
http://www.research.att.com/~njas/sequences/table?a=130799
) and AFAICS the only way to find out where the anti-divisors of a
number n will start is to spot violations of strict increasing
monotony
(which is of course not failsafe,  e.g. if a number >2 would have no
antidivisors, or some number would have its largest antidiv. smaller
than the least antidiv of its successor....)

IMHO all these sequences need much clarification and cleanup of definitions.
Insofar more as the "authorative" definition seems to be on an
unavailable web page (and the version I can found via the "wayback"
machine does not contain a clear definition either - again several
"Or, to put it another way..." etc). All in all there is a heavy smell
of *very* original research in the air around this.

M.H.

On 7/20/07, Maximilian Hasler <maximilian.hasler at gmail.com> wrote:
> It appears to me that the definition
>
> %C A066272 If an odd number d in the range 1 < d < n divides N where N
> is any one of 2n-1, 2n or 2n+1 then N/d is called an anti-divisor of
> n.
>
> is not equivalent to your definition:
>
> > Non-divisor: a number k which does not divide a given
> > number x. Anti-divisor: a non-divisor k of x with the
> > property that k is an odd divisor of 2x-1 or 2x+1, or
> > an even divisor of 2x.
>
> According to the first definition, n=3 cannot have an anti-divisor
> since there is no odd d, 1<d<n.
>
> M.H.
>