OFFSET
1,2
COMMENTS
Two circulant graphs are Cayley isomorphic if there is a d, which is necessarily prime to n, that transforms through multiplication modulo n the step values of one graph into those of the other. For squarefree n this is the only way that two circulant graphs can be isomorphic (See A049287).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
V. A. Liskovets and R. Poeschel, On the enumeration of circulant graphs of prime-power and squarefree orders.
MATHEMATICA
IsLeastPoint[s_, f_] := Module[{t = f[s]}, While[t > s, t=f[t]]; Boole[s == t]];
c[n_, k_] := Sum[IsLeastPoint[u, Abs[Mod[#*k + Quotient[n, 2], n] - Quotient[n, 2]]&], {u, 1, n/2}];
a[n_] := If[n < 3, n, Sum[If[GCD[k, n] == 1, 2^c[n, k], 0]*2/EulerPhi[n], {k, 1, n/2}]];
Array[a, 50] (* Jean-François Alcover, Jun 12 2017, translated from PARI *)
PROG
(PARI)
IsLeastPoint(s, f)={my(t=f(s)); while(t>s, t=f(t)); s==t}
C(n, k)=sum(u=1, n/2, IsLeastPoint(u, v->abs((v*k+n\2)%n-n\2)));
a(n)=if(n<3, n, sum(k=1, n/2, if (gcd(k, n)==1, 2^C(n, k), 0))*2/eulerphi(n));
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Apr 22 2017
STATUS
approved