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A069739 Size of the key space for isomorphism verification of circulant graphs of order n. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
Multiplicative with a(p^m) = Catalan(m) (A000108). Coincides with A066060 up to n=63 except for n=32.
REFERENCES
M. Muzychuk, A solution of the isomorphism problem for circulant graphs, Proc. London Math. Soc. (3) 88 (2004), no. 1, 1-41.
LINKS
FORMULA
a(n) = prod_p Catalan(m_p) where n=prod_p p^(m_p), p|n prime.
From Antti Karttunen, May 28-29 2017: (Start)
a(1) = 1; for n > 1, a(n) = A000108(A067029(n)) * a(A028234(n)).
a(n) = A246596(A156552(n)). (End)
MAPLE
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:
seq(A069739(n), n=1..90) ; # R. J. Mathar, Feb 08 2011
MATHEMATICA
Table[Times @@ Map[CatalanNumber, FactorInteger[n][[All, -1]]], {n, 90}] (* Michael De Vlieger, May 28 2017 *)
PROG
(Scheme) (define (A069739 n) (if (= 1 n) n (* (A000108 (A067029 n)) (A069739 (A028234 n))))) ;; Antti Karttunen, May 28 2017
CROSSREFS
Sequence in context: A351861 A343233 A155586 * A066060 A008550 A064094
KEYWORD
mult,easy,nonn
AUTHOR
Valery A. Liskovets, Apr 15 2002
STATUS
approved

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Last modified March 29 06:15 EDT 2024. Contains 371265 sequences. (Running on oeis4.)