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 A285620 Number of circulant graphs on n vertices up to Cayley isomorphism. 3
 1, 2, 2, 4, 3, 8, 4, 12, 8, 20, 8, 48, 14, 48, 44, 88, 36, 192, 60, 336, 200, 416, 188, 1344, 424, 1400, 944, 3104, 1182, 8768, 2192, 8784, 6768, 16460, 11144, 46848, 14602, 58288, 44424, 138432, 52488, 355200, 99880, 432576, 351712, 762608, 364724, 2151936, 798960 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A049287, A056391 (circulant digraphs), A049297, A038782. Sequence in context: A285330 A048676 A049287 * A185959 A006799 A056429 Adjacent sequences:  A285617 A285618 A285619 * A285621 A285622 A285623 KEYWORD nonn AUTHOR Andrew Howroyd, Apr 22 2017 STATUS approved

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Last modified July 17 20:45 EDT 2019. Contains 325109 sequences. (Running on oeis4.)