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2*p^2, for p an odd prime.
12

%I #41 Dec 17 2021 03:14:58

%S 18,50,98,242,338,578,722,1058,1682,1922,2738,3362,3698,4418,5618,

%T 6962,7442,8978,10082,10658,12482,13778,15842,18818,20402,21218,22898,

%U 23762,25538,32258,34322,37538,38642,44402,45602,49298,53138,55778,59858

%N 2*p^2, for p an odd prime.

%C For these numbers m, there are precisely 5 groups of order m, hence it is a subsequence of A054397. The 5 groups are C_{2*p^2}, C_2 X (C_p X C_p), C_p^2 : C_2 ~ D_{2*p^2}, and two non-isomorphic groups (C_p X C_p) : C_2, where C, D mean cyclic, dihedral groups of the stated order; the symbols ~, X and : mean isomorphic to, direct and semidirect products respectively. - _Bernard Schott_, Dec 10 2021

%D Pascal Ortiz, Exercices d'Algèbre, Collection CAPES / Agrégation, Ellipses, problème 1.35, pp. 70-74, 2004.

%H Harvey P. Dale, <a href="/A143928/b143928.txt">Table of n, a(n) for n = 1..1000</a>

%H Michael Hilgemann and Siu-Hung Ng, <a href="http://arxiv.org/abs/0809.0699">Hopf algebras of dimension 2p^2</a>, arXiv:0809.0699 [math.QA], 2008.

%F a(n) = A079704(n+1) for n>0.

%e a(1) = 2*A065091(1)^2 = 2*3^2 = 18.

%e a(2) = 2*A065091(2)^2 = 2*5^2 = 50.

%e a(3) = 2*A065091(3)^2 = 2*7^2 = 98.

%t 2#^2&/@Prime[Range[2,40]] (* _Harvey P. Dale_, Jul 23 2021 *)

%o (Python)

%o from sympy import prime

%o def a(n): return 2*prime(n+1)**2

%o print([a(n) for n in range(1, 40)]) # _Michael S. Branicky_, Dec 10 2021

%Y Subsequence of A079704.

%Y Cf. A054397, A065091.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Sep 05 2008