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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 (list; graph; refs; listen; history; text; internal format)
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 13-19.

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) 367-371.

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), 78-81.

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

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Last modified September 20 00:33 EDT 2020. Contains 337216 sequences. (Running on oeis4.)