Concatenated anti-divisors

[Jonathan Post]

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.

There are no anti-divisors of 1 and 2.

See A066272 for an equivalent definition and also the
number of terms in each row.

Now, if we concatenate antidivisors of integers n>2, we have an
anti-divisor analogue of A106708.

This should be easy for someone to Mathematica-ize and extend, and
leads to the same kind of fun questions as its origin does.

===========
n  a(n)  factorization
3  2     prime
4  3     prime
5  23    prime
6  4     2^2
7  235   5 * 47
8  35    5 * 7
9  26    2 * 13
10 347   prime
11 237   3 * 79
12 58    2 * 29
13 2359  7 * 337
14 349   prime
15 2610  2 * 3^2 * 5 * 29
16 311   prime
17 235711  7 * 151 * 223
18 45712 2^4 * 2857
19 2313  3^2 * 257
20 3813  3 * 31 * 41
===========

--- The On-Line Encyclopedia of Integer Sequences
<oeis at research.att.com> wrote:

 The following is a copy of the email message that
 was sent to njas
  Subject: NEW SEQUENCE FROM Jonathan Vos Post

 %I A000001
 %S A000001 2, 3, 23, 4, 235, 35, 26, 347, 237, 58,
 2359, 349, 2610, 311, 235711, 45712, 2313, 3813
 %N A000001 Replace n by the concatenation of its
 antidivisors.
 %C A000001 Number of antidivisors concatened to form
 a(n) is A066272(n). We may consider prime values of
 the concatenated antidivisor sequence, and we may
 iterate it, i.e. n, a(n), a(a(n)), a(a(a(n))) which
 leads to questions of trajectory, cycles, fixed
 points.
 %e A000001 Anti-divisors of 3 through 20:
 3: 2, so a(3) = 2.
 4: 3, so a(4) = 3.
 5: 2, 3, so a(5) = 23.
 6: 4, so a(6) = 4.
 7: 2, 3, 5, so a(7) = 235.
 17: 2, 3, 5, 7, 11, so a(17) = 235711
 %Y A000001 Cf. A037278, A066272, A120712, A106708,
 A130799.
 %O A000001 3
 %K A000001 ,base,easy,more,nonn,
 %A A000001 Jonathan Vos Post (jvospost2 at yahoo.com),
 Jul 20 2007
 RH
 RA 192.20.225.32