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A034382 Number of labeled Abelian groups of order n. 6
1, 2, 3, 16, 30, 360, 840, 15360, 68040, 907200, 3991680, 159667200, 518918400, 14529715200, 163459296000, 4250979532800, 22230464256000, 1200445069824000, 6758061133824000, 405483668029440000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

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

Sugarknri et al., Number of labeled Abelian groups of order n. MathOverflow, 2019.

Index entries for sequences related to enumerating 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).

CROSSREFS

Cf. A000688, A034381, A034383, A058159.

Sequence in context: A102882 A085734 A302837 * A034383 A072684 A073633

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

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Last modified October 20 10:00 EDT 2019. Contains 328257 sequences. (Running on oeis4.)