cp's OEIS Frontend

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.

A337706 Possible values for the product of the orders of all elements of a finite group.

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%I A337706 #13 Oct 24 2020 16:52:37
%S A337706 1,2,8,9,32,72,128,512,625,648,2048,6561,8192,20000,32768,41472,52488,
%T A337706 117649,131072,524288,2654208,3359232,4782969,8388608,12500000,
%U A337706 15059072,33554432,134217728,214990848,536870912,2147483648,2448880128
%N A337706 Possible values for the product of the orders of all elements of a finite group.
%C A337706 The product of the orders of all elements of a finite group G is denoted by P(G).
%C A337706 P(A X B) = P(A)^|B|P(B)^|A| for finite groups A and B of coprime orders.
%C A337706 P(G) < P(C_n) for every noncyclic finite group G of order n.
%H A337706 M. Farrokhi D. G., <a href="/A337706/b337706.txt">Table of n, a(n) for n = 1..2733</a>
%H A337706 M. Garonzi and M. Patassini, <a href="https://doi.org/10.1080/00927872.2016.1172621">Inequalities detecting structural properties of a finite group</a>, Comm. Algebra (2017) 45(2), 677-687.
%H A337706 M. Herzog, P. Longobardi, and M. Maj, <a href="https://doi.org/10.1007/978-981-13-2047-7_4">Properties of finite and periodic groups determined by their element of orders (a survey)</a>, Group theory and computation, 59-90, Indian Stat. Inst. Ser., Springer, Singapore, 2018.
%e A337706 P(C_6) = 1*2*3*3*6*6 = 648.
%o A337706 (GAP) Product(List(G, Order))
%K A337706 nonn
%O A337706 1,2
%A A337706 _M. Farrokhi D. G._, Sep 16 2020