Reinhard.Zumkeller@gmail.com
                                                        May 24 2010
                                                        a178254.txt

A178254  Example for n=42
=======  ================

The proper divisors of 42 = 2*3*7:  1, 2, 3, 7, 6, 14, and 21;
there are A178254(42)=36 permutations such that adjacent elements 
are coprime.

01  [2, 21, 1, 6, 7, 3, 14]
02  [2, 21, 1, 14, 3, 7, 6]
03  [3, 14, 1, 6, 7, 2, 21]
04  [3, 14, 1, 21, 2, 7, 6]
05  [6, 1, 14, 3, 7, 2, 21]
06  [6, 1, 21, 2, 7, 3, 14]
07  [6, 7, 1, 14, 3, 2, 21]
08  [6, 7, 1, 21, 2, 3, 14]
09  [6, 7, 2, 3, 14, 1, 21]
10  [6, 7, 2, 21, 1, 3, 14]
11  [6, 7, 2, 21, 1, 14, 3]
12  [6, 7, 3, 2, 21, 1, 14]
13  [6, 7, 3, 14, 1, 2, 21]
14  [6, 7, 3, 14, 1, 21, 2]
15  [7, 6, 1, 14, 3, 2, 21]
16  [7, 6, 1, 21, 2, 3, 14]
17  [14, 1, 6, 7, 3, 2, 21]
18  [14, 1, 21, 2, 3, 7, 6]
19  [14, 3, 1, 6, 7, 2, 21]
20  [14, 3, 1, 21, 2, 7, 6]
21  [14, 3, 2, 7, 6, 1, 21]
22  [14, 3, 2, 21, 1, 6, 7]
23  [14, 3, 2, 21, 1, 7, 6]
24  [14, 3, 7, 2, 21, 1, 6]
25  [14, 3, 7, 6, 1, 2, 21]
26  [14, 3, 7, 6, 1, 21, 2]
27  [21, 1, 6, 7, 2, 3, 14]
28  [21, 1, 14, 3, 2, 7, 6]
29  [21, 2, 1, 6, 7, 3, 14]
30  [21, 2, 1, 14, 3, 7, 6]
31  [21, 2, 3, 7, 6, 1, 14]
32  [21, 2, 3, 14, 1, 6, 7]
33  [21, 2, 3, 14, 1, 7, 6]
34  [21, 2, 7, 3, 14, 1, 6]
35  [21, 2, 7, 6, 1, 3, 14]
36  [21, 2, 7, 6, 1, 14, 3]


Generally for p, q, and r prime, with p < q < r
(multiplication signs omitted):

01  [p, qr, 1, pq, r, q, pr]
02  [p, qr, 1, pr, q, r, pq]
03  [q, pr, 1, pq, r, p, qr]
04  [q, pr, 1, qr, p, r, pq]
05  [pq, 1, pr, q, r, p, qr]
06  [pq, 1, qr, p, r, q, pr]
07  [pq, r, 1, pr, q, p, qr]
08  [pq, r, 1, qr, p, q, pr]
09  [pq, r, p, q, pr, 1, qr]
10  [pq, r, p, qr, 1, q, pr]
11  [pq, r, p, qr, 1, pr, q]
12  [pq, r, q, p, qr, 1, pr]
13  [pq, r, q, pr, 1, p, qr]
14  [pq, r, q, pr, 1, qr, p]
16  [r, pq, 1, pr, q, p, qr]
15  [r, pq, 1, qr, p, q, pr]
17  [pr, 1, pq, r, q, p, qr]
18  [pr, 1, qr, p, q, r, pq]
19  [pr, q, 1, pq, r, p, qr]
20  [pr, q, 1, qr, p, r, pq]
21  [pr, q, p, r, pq, 1, qr]
22  [pr, q, p, qr, 1, pq, r]
23  [pr, q, p, qr, 1, r, pq]
24  [pr, q, r, p, qr, 1, pq]
25  [pr, q, r, pq, 1, p, qr]
26  [pr, q, r, pq, 1, qr, p]
27  [qr, 1, pq, r, p, q, pr]
28  [qr, 1, pr, q, p, r, pq]
29  [qr, p, 1, pq, r, q, pr]
30  [qr, p, 1, pr, q, r, pq]
31  [qr, p, q, r, pq, 1, pr]
32  [qr, p, q, pr, 1, pq, r]
33  [qr, p, q, pr, 1, r, pq]
34  [qr, p, r, q, pr, 1, pq]
35  [qr, p, r, pq, 1, q, pr]
36  [qr, p, r, pq, 1, pr, q]

Seen symbolically the defining property can be stated 
as ?all permutations of (1, p, q, r, pq, pr, qr) such 
that adjacent words have no common letter?.