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

1,4

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

Table of n, a(n) for n=1..49.

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

Cf. A274847, A018216, A289445.

Sequence in context: A325099 A370777 A088177 * A028507 A096226 A155980

Adjacent sequences: A335914 A335915 A335916 * A335918 A335919 A335920

Keyword

nonn,more

Author

David A. Nash, Jun 29 2020

Status

approved