cp's OEIS Frontend

A335917 a(n) is the number of similarity classes of abelian groups with exactly n subgroups (see reference for precise definition of similarity classes).

%I A335917 #13 Jul 15 2020 12:36:39
%S A335917 1,1,1,2,2,3,1,5,2,5,2,5,1,6,4,9,2,7,1,11,2,6,3,11,3,8,4,9,3,14,1,16,
%T A335917 3,6,4,15,2,8,2,21,2,13,2,13,8,6,2,23,4
%N A335917 a(n) is the number of similarity classes of abelian groups with exactly n subgroups (see reference for precise definition of similarity classes).
%C A335917 See Slattery references for a precise definition of similarity.
%C A335917 See Betz and Nash first reference for proof of the first 22 terms.
%C A335917 See Betz and Nash second reference for proof of terms 23--49.
%H A335917 Alexander Betz and David A. Nash, <a href="https://arxiv.org/abs/2006.11315">Classifying groups with a small number of subgroups</a>, arXiv:2006.11315 [math.GR], (2020).
%H A335917 Alexander Betz and David A. Nash, <a href="https://www.researchgate.net/publication/342918790_A_note_on_abelian_groups_with_fewer_than_50_subgroups">A note on abelian groups with fewer than 50 subgroups</a>, preprint, (2020).
%H A335917 G. A. Miller, <a href="http://www.pnas.org/content/25/7/367.full.pdf">Groups having a small number of subgroups</a>, Proc. Natl. Acad. Sci. U S A, vol. 25 (1939) 367-371.
%H A335917 M. C. Slattery, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.123.1.78">On a property motivated by groups with a specified number of subgroups</a>, Amer. Math. Monthly, 123 (2016), 78-81.
%H A335917 M. C. Slattery, <a href="http://arxiv.org/abs/1607.01834">Groups with at most twelve subgroups</a>, arXiv:1607.01834 [math.GR], 2016-2020.
%e A335917 For n = 6, a(6) = 3 and the three similarity classes of abelian groups with exactly six subgroups are Z_{p^5}, Z_{p^2q}, and Z_3 X Z_3.
%Y A335917 Cf. A274847, A018216, A289445.
%K A335917 nonn,more
%O A335917 1,4
%A A335917 _David A. Nash_, Jun 29 2020