Search: id:A058890
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%I A058890
%S A058890 0,2,9,10,15,11,14,14,15,17,22,18,26,16,21,22,34,17,38,25,23,24,46,
%T A058890 22,35,28,33,24,58,23,62,38,31,36,29,24,74,40,35,29,82,25,86,32,27,
%U A058890 48,94,30
%N A058890 Smallest number of nodes in a graph whose automorphism group is cyclic 
               of order n.
%D A058890 William C. Arlinghaus, The classification of minimal graphs with given 
               Abelian automorphism group, Memoirs of the American Mathematical 
               Society, Number 330, September 1985.
%D A058890 F. Harary, Graph Theory, Page 176, Problem 14.7.
%F A058890 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)
%F A058890 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.
%F A058890 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.
%Y A058890 Cf. A080803.
%Y A058890 Sequence in context: A031443 A051017 A078180 this_sequence A047468 A032929 
               A046975
%Y A058890 Adjacent sequences: A058887 A058888 A058889 this_sequence A058891 A058892 
               A058893
%K A058890 nonn,nice,easy
%O A058890 1,2
%A A058890 N. J. A. Sloane (njas(AT)research.att.com), Jan 08 2001
%E A058890 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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