%I A086595
%S A086595 1,1,2,2,12,4,72,72,720,576,22032,7776,476928,400896,6352992,8515584,
%T A086595 805146624,279023616,36481536000,23627980800,881012367360,1065509240832,
%U A086595 192859121664000,65362194432000,10489384048435200
%N A086595 Number of ways to arrange the numbers 1..n in a circle such that every 
               two adjacent numbers are relatively prime.
%C A086595 a(n) is also the number of permutations of 2..n such that every two adjacent 
               numbers are relatively prime.
%F A086595 For prime p, a(p)=A076220(p-1) - Max Alekseyev (maxale(AT)gmail.com), 
               Jun 13 2005
%e A086595 a(6) = 4 since there are 4 ways to arrange 1,2,3,4,5,6 in a circle such 
               that every two adjacent numbers are relatively prime: 1-2-3-4-5-6-1, 
               1-4-3-2-5-6-1, 1-6-5-2-3-4-1, 1-6-5-4-3-2-1.
%o A086595 (PARI) {A086595(n) = local(d, A, r, M); A=matrix(n,n,i,j,if(gcd(i,j)==1,
               1,0)); r=0; forstep(s=1,2^n-1,2,M=vecextract(A,s,s)^n; d=matsize(M)[1]; 
               r+=(-1)^(n-d)*M[1,1]);r} (Alekseyev)
%Y A086595 Cf. A076220.
%Y A086595 Sequence in context: A058044 A128269 A109813 this_sequence A013605 A073768 
               A096855
%Y A086595 Adjacent sequences: A086592 A086593 A086594 this_sequence A086596 A086597 
               A086598
%K A086595 nonn
%O A086595 1,3
%A A086595 Lior Manor (lior.manor(AT)gmail.com) Jul 23 2003
%E A086595 a(15)=6352992 and a(16)=8515584 from Ray Chandler (rayjchandler(AT)sbcglobal.net) 
               and Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), Apr 10 2005
%E A086595 Many more terms from Max Alekseyev (maxale(AT)gmail.com), Jun 13 2005