Finite(?) Sequence (involving divisors)

[hv at crypt.org]

sequence, all d <= m that divide n must be non-isolated. This requires in
sequence is 4.
sequence, and the only remaining members of the sequence must be oblong.
show that for sufficiently large m, 2b/3 is too large and 2b/5 is too
small to be adjacent to a/2.
show that the sequence is as given.
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Date: Fri, 2 Nov 2007 00:28:40 -0700
From: "Max Alekseyev" <maxale at gmail.com>
To: seqfan at ext.jussieu.fr
Subject: invertible matrices over Z_m
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The number of invertible matrices over Z_m is given is the paper:

J. Overbey, W. Traves, J. Wojdylo "On the Keyspace of the Hill Cipher"
http://jeff.over.bz/papers/undergrad/on-the-keyspace-of-the-hill-cipher.pdf

along with some other nice formulas.

It seems that this paper is not referred from OEIS while it joins a
number of sequences under a general formula and may provide new
sequences (see below).
As I have no time to work on this paper now, I'd like to ask somebody
to bring all useful information (basically references and new
sequences) from this paper to OEIS.

As a sneak pick I suggest the following straightforward PARI/GP
implementation of the formula from Theorem 2.3.3:

{ g(d,m) = local(f=factorint(m)); prod(i=1,matsize(f)[1],
f[i,1]^((f[i,2]-1)*d^2) * prod(k=0,d-1, f[i,1]^d-f[i,1]^k) ) }

For d=0..5, m=1..5 it gives:

? matrix(6,5,d,m,g(d-1,m))
%1 =
[1 1 1 1 1]
[1 1 2 2 4]
[1 6 48 96 480]
[1 168 11232 86016 1488000]
[1 20160 24261120 1321205760 116064000000]
[1 9999360 475566474240 335522845163520 226614960000000000]

Zeroth row (d=0) is all-ones A000012.
First row (d=1) gives A000010 (Euler totient function)
Second row (d=2) is A000252
Third row (d=3) is A064767

First seven columns (m=1..7) are A000012, A002884, A053290, A065128,
A053292, A065498, A053293.

For sequences A065128 and A065498, I suggest to prepend 1 to this
sequence and change their offset to 0 to be consistent with the other
similar sequences.

Regards,
Max