This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A034382 #29 Nov 25 2022 07:23:47 %S A034382 1,2,3,16,30,360,840,15360,68040,907200,3991680,159667200,518918400, %T A034382 14529715200,163459296000,4250979532800,22230464256000, %U A034382 1200445069824000,6758061133824000,405483668029440000 %N A034382 Number of labeled Abelian groups of order n. %H A034382 Max Alekseyev, <a href="/A034382/b034382.txt">Table of n, a(n) for n = 1..100</a> %H A034382 Hy Ginsberg, <a href="https://arxiv.org/abs/2211.13204">Totally Symmetric Quasigroups of Order 16</a>, arXiv:2211.13204 [math.CO], 2022. %H A034382 C. J. Hillar and D. Rhea. <a href="https://www.jstor.org/stable/27642365">Automorphisms of finite Abelian groups</a>. American Mathematical Monthly 114:10 (2007), 917-923. Preprint <a href="https://arxiv.org/abs/math/0605185">arXiv:math/0605185</a> [math.GR], 2006. %H A034382 Sugarknri et al., <a href="https://math.stackexchange.com/q/3355137">Number of labeled Abelian groups of order n</a>, Mathematics Stack Exchange, 2019. %H A034382 <a href="/index/Gre#groups">Index entries for sequences related to groups</a> %F A034382 a(n) = A058162(n) * n. %F A034382 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). %Y A034382 Cf. A000688, A034381, A034383, A058159. %K A034382 nonn %O A034382 1,2 %A A034382 _Christian G. Bower_ %E A034382 a(16) corrected by _Max Alekseyev_, Sep 12 2019