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Search: id:A058890
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| A058890 |
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Smallest number of nodes in a graph whose automorphism group is cyclic of order n. |
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+0
2
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| 0, 2, 9, 10, 15, 11, 14, 14, 15, 17, 22, 18, 26, 16, 21, 22, 34, 17, 38, 25, 23, 24, 46, 22, 35, 28, 33, 24, 58, 23, 62, 38, 31, 36, 29, 24, 74, 40, 35, 29, 82, 25, 86, 32, 27, 48, 94, 30
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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William C. Arlinghaus, The classification of minimal graphs with given Abelian automorphism group, Memoirs of the American Mathematical Society, Number 330, September 1985.
F. Harary, Graph Theory, Page 176, Problem 14.7.
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FORMULA
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a(2) = 2; for r > 1, a(2^r) = 2^r + 6; for p = 3 or 5 and r > 0, a(p^r) = p^r + 2p; for p prime >= 7 and r > 0, a(p^r) = p^r + p. (Harary)
a(n) = a(p1^r1 p2^r2 ... pk^rk) = a(p1^r1) + ... + a(pn^rn) - F where F is a "correction factor" which depends on the exponents of the primes 2, 3 and 5 in the prime factorization of the number n. Call these values n2, n3 and n5 respectively.
The correction factor F is 0 if n3 = 0 (so unless 3 divides n, the upper bound is exact); 4 if n2 = 2, n3 >= 1 and n5 = 1; 3 if n2 != 2, n3 >=1 and n5 = 1; 1 if n2 = 2, n3 >= 1 and n5 != 1; 1 if n2 >= 2, n3 = 1 and n5 != 1; 0 otherwise.
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CROSSREFS
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Cf. A080803.
Sequence in context: A031443 A051017 A078180 this_sequence A047468 A032929 A046975
Adjacent sequences: A058887 A058888 A058889 this_sequence A058891 A058892 A058893
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 08 2001
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EXTENSIONS
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Additional comments and more terms from David Wasserman (dwasserm(AT)earthlink.com) and Gordon Royle (gordon(AT)maths.uwa.edu.au), Jun 09 2002
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