A335917 a(n) is the number of similarity classes of abelian groups with exactly n subgroups (see reference for precise definition of similarity classes).
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, 3, 6, 4, 15, 2, 8, 2, 21, 2, 13, 2, 13, 8, 6, 2, 23, 4
Offset: 1
Examples
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.
Links
- Alexander Betz and David A. Nash, Classifying groups with a small number of subgroups, arXiv:2006.11315 [math.GR], (2020).
- Alexander Betz and David A. Nash, A note on abelian groups with fewer than 50 subgroups, preprint, (2020).
- G. A. Miller, Groups having a small number of subgroups, Proc. Natl. Acad. Sci. U S A, vol. 25 (1939) 367-371.
- M. C. Slattery, On a property motivated by groups with a specified number of subgroups, Amer. Math. Monthly, 123 (2016), 78-81.
- M. C. Slattery, Groups with at most twelve subgroups, arXiv:1607.01834 [math.GR], 2016-2020.
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