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A335917
a(n) is the number of similarity classes of abelian groups with exactly n subgroups (see reference for precise definition of similarity classes).
0
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
1,4
COMMENTS
See Slattery references for a precise definition of similarity.
See Betz and Nash first reference for proof of the first 22 terms.
See Betz and Nash second reference for proof of terms 23--49.
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.
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
David A. Nash, Jun 29 2020
STATUS
approved