A034382 Number of labeled Abelian groups of order n.

1, 2, 3, 16, 30, 360, 840, 15360, 68040, 907200, 3991680, 159667200, 518918400, 14529715200, 163459296000, 4250979532800, 22230464256000, 1200445069824000, 6758061133824000, 405483668029440000

Offset

1,2

Links

Max Alekseyev, Table of n, a(n) for n = 1..100

Hy Ginsberg, Totally Symmetric Quasigroups of Order 16, arXiv:2211.13204 [math.CO], 2022.

C. J. Hillar and D. Rhea. Automorphisms of finite Abelian groups. American Mathematical Monthly 114:10 (2007), 917-923. Preprint arXiv:math/0605185 [math.GR], 2006.

Sugarknri et al., Number of labeled Abelian groups of order n, Mathematics Stack Exchange, 2019.

Index entries for sequences related to groups

Formula

a(n) = A058162(n) * n.

a(n) = Sum n!/|Aut(G)|, where the sum is taken over the different products G of cyclic groups with |G|=n. Formula for |Aut(G)| is given by Hillar and Rhea (2007). Another formula is given by Sugarknri (2019).

Crossrefs

Cf. A000688, A034381, A034383, A058159.

Sequence in context: A359391 A085734 A302837 * A034383 A350025 A072684

Adjacent sequences: A034379 A034380 A034381 * A034383 A034384 A034385

Keyword

nonn

Author

Christian G. Bower

Extensions

a(16) corrected by Max Alekseyev, Sep 12 2019

Status

approved