

A274847


a(n) = number of similarity classes of groups with exactly n subgroups (see reference for precise definition of similarity classes).


2



1, 1, 1, 2, 2, 5, 1, 7, 2, 12, 4, 11, 1, 17, 8, 22, 3, 22, 5
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OFFSET

1,4


COMMENTS

See Slatterly references for precise definition of similarity classes and a proof of the first 12 terms.
See Betz and Nash for correction of a(10) and proof of terms 1319.


LINKS

Table of n, a(n) for n=1..19.
G. A. Miller, Groups having a small number of subgroups, Proc. Natl. Acad. Sci. U S A, vol. 25 (1939) 367371.
David A. Nash, Alexander Betz, Classifying groups with a small number of subgroups, arXiv:2006.11315 [math.GR], 2020.
M. C. Slattery, On a property motivated by groups with a specified number of subgroups, Amer. Math. Monthly, 123 (2016), 7881.
M. C. Slattery, Groups with at most twelve subgroups, arXiv:1607.01834 [math.GR], (2016).
Alexander Betz and David A. Nash, Classifying groups with a small number of subgroups, arXiv:2006.11315 [math.GR], (2020).


EXAMPLE

For n = 6 the a(6) = 5 similarity classes of groups with 6 subgroups are Z_{p^5}, Z_p X Z_{q^2}, Z_3 X Z_3, S_3, Q_8.


CROSSREFS

Cf. A018216, A289445.
Sequence in context: A128932 A286150 A071950 * A165922 A337293 A307834
Adjacent sequences: A274844 A274845 A274846 * A274848 A274849 A274850


KEYWORD

nonn,more,changed


AUTHOR

Michael C Slattery, Jul 08 2016


EXTENSIONS

Correction of a(10) and extension to 19 terms by David A. Nash, Jun 29 2020


STATUS

approved



