This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A341825 #14 Mar 04 2021 14:36:31 %S A341825 2,3,0,4,0,6,0,7,0,2,0,9,0,0,0,11,0,4,0,7,0,2,0,22,0,0,0,2,0,2,0,19,0, %T A341825 0,0,12,0,0,0,14,0,7,0,3,0,2,0 %N A341825 Number of finite groups G with |Aut(G)| = n. %C A341825 The smallest odd index n > 1 for which a(n) > 0 is 2187 = 3^7 (see A340521). %C A341825 There exist even indices n that are not values taken by totient function phi (A002202) for which a(n) > 0. For example, John Bray has produced a group G that is the semidirect product 19:9 of order 3^2*19 = 171 such that |Aut(G)| = 1026 = 2*3^3*19. %H A341825 D. MacHale and R. Sheehy, <a href="http://www.jstor.org/stable/40656888">Finite groups with few automorphisms</a>, Mathematical Proceedings of the Royal Irish Academy, Vol. 104A, No. 2 (December 2004), 231-238. %F A341825 a(2) = 3, a(p) = 0 if p odd prime. %F A341825 a(A002202(n)) > 0, since |Aut(C_n)| = phi(n). %e A341825 a(6) = 6, because there are six groups G with |Aut(G)| = 6. Four cyclic groups: Aut(C_7) = Aut(C_9) = Aut(C_14) = Aut(C_18) ~~ C_6, and also Aut(C_2 x C_2) = Aut(S_3) ~~ S_3, where ~~ stands for “isomorphic to”. - _Bernard Schott_, Mar 02 2021 %e A341825 a(8) = 7, because there are seven groups G with |Aut(G)| = 8. %Y A341825 Cf. A002202, A137315, A340521, A341823, A341824. %K A341825 nonn,more %O A341825 1,1 %A A341825 _Des MacHale_, Mar 02 2021