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A069739
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Size of the key space for isomorphism verification of circulant graphs of order n.
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5
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1, 1, 1, 2, 1, 1, 1, 5, 2, 1, 1, 2, 1, 1, 1, 14, 1, 2, 1, 2, 1, 1, 1, 5, 2, 1, 5, 2, 1, 1, 1, 42, 1, 1, 1, 4, 1, 1, 1, 5, 1, 1, 1, 2, 2, 1, 1, 14, 2, 2, 1, 2, 1, 5, 1, 5, 1, 1, 1, 2, 1, 1, 2, 132, 1, 1, 1, 2, 1, 1, 1, 10, 1, 1, 2, 2, 1, 1, 1, 14, 14, 1, 1, 2, 1, 1, 1, 5, 1, 2
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OFFSET
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1,4
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COMMENTS
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Multiplicative with a(p^m) = Catalan(m) (A000108). Coincides with A066060 up to n=63 except for n=32.
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REFERENCES
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M. Muzychuk, A solution of the isomorphism problem for circulant graphs, Proc. London Math. Soc. (3) 88 (2004), no. 1, 1-41.
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LINKS
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FORMULA
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a(n) = prod_p Catalan(m_p) where n=prod_p p^(m_p), p|n prime.
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MAPLE
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A000108 := proc(n) binomial(2*n, n)/(n+1) ; end proc:
A069739 := proc(n) local ifa; if n = 1 then 1; else ifa := ifactors(n)[2] ; mul( A000108(op(2, f)), f=ifa) ; end if; end proc:
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MATHEMATICA
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Table[Times @@ Map[CatalanNumber, FactorInteger[n][[All, -1]]], {n, 90}] (* Michael De Vlieger, May 28 2017 *)
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PROG
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CROSSREFS
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KEYWORD
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mult,easy,nonn
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AUTHOR
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STATUS
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approved
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