%I A102381
%S A102381 1,2,6,8,60,24,504,576,6480,5760,242352,93312,6200064,5612544,95294880,
%T A102381 136249344,13687492608,5022425088,693149184000,472559616000,
%U A102381 18501259714560,23441203298304,4435759798272000,1568692666368000
%N A102381 Number of permutations of 1..n in which every pair of adjacent numbers 
               as well as the first and the last entries are relatively prime.
%C A102381 a(n)=n*A086595(n).
%H A102381 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%e A102381 a(4)=8 because we have 1234, 1432, 2143, 2341, 3214, 3412, 4123 and 4321.
%p A102381 with(combinat): for n from 1 to 7 do P:=permute(n): ct:=0: for j from 
               1 to n! do if add(gcd(P[j][i+1],P[j][i]),i=1..n-1)=n-1 and gcd(P[j][1],
               P[j][n])=1 then ct:=ct+1 else ct:=ct fi od: a[n]:=ct: od: seq(a[n],
               n=1..7);
%Y A102381 Cf. A086595, A076220.
%Y A102381 Sequence in context: A098239 A140257 A053938 this_sequence A075998 A007849 
               A100621
%Y A102381 Adjacent sequences: A102378 A102379 A102380 this_sequence A102382 A102383 
               A102384
%K A102381 nonn
%O A102381 1,2
%A A102381 Emeric Deutsch (in collaboration with R. Chandler, V. Jovovic, L. Quet, 
               Z. Seidov and J. Zucker) (deutsch(AT)duke.poly.edu), Apr 09 2005
%E A102381 a(15)=95294880 and a(16)=136249344 from Ray Chandler (rayjchandler(AT)sbcglobal.net) 
               and Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), Apr 12 2005
%E A102381 Many more terms from Max Alekseyev (maxale(AT)gmail.com), Jun 13 2005