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 A340521 List of possible orders of automorphism groups of finite groups. 4
 1, 2, 4, 6, 8, 10, 12, 16, 18, 20, 22, 24, 28, 30, 32, 36, 40, 42, 44, 46, 48, 52, 54, 56, 58, 60 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The terms shown here match the initial terms of all of A002174, A002202, A049225, but this is a strictly different sequence since it is known that it contains 3^7 = 2187 (which is the smallest odd term greater than 1), whereas for the other three sequences all terms greater than 1 are even. This is a supersequence of A002202 since |Aut(Z/nZ)| = phi(n). - Jianing Song, Feb 05 2021 John Bray has produced a group G of order 3^2*19 = 171 such that |Aut G| = 1026 = 2.3^3.19. So 1026 is in the present sequence but is not in A002202. So the present sequence contains both odd and even terms not in A002202. - Des MacHale, Feb 10 2021 For more about this problem, see the references in A137315. LINKS D. MacHale and R. Sheehy, Finite groups with few automorphisms, Mathematical Proceedings of the Royal Irish Academy, Vol. 104A, No. 2 (December 2004), 231-238. CROSSREFS Cf. A002174, A002202, A049225, A137315. Sequence in context: A011860 A259278 A049445 * A002174 A002202 A049225 Adjacent sequences:  A340518 A340519 A340520 * A340522 A340523 A340524 KEYWORD nonn,more AUTHOR Des MacHale, Feb 05 2021 STATUS approved

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Last modified May 11 03:49 EDT 2021. Contains 343784 sequences. (Running on oeis4.)