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 A143928 2*p^2, for p an odd prime. 10
 18, 50, 98, 242, 338, 578, 722, 1058, 1682, 1922, 2738, 3362, 3698, 4418, 5618, 6962, 7442, 8978, 10082, 10658, 12482, 13778, 15842, 18818, 20402, 21218, 22898, 23762, 25538, 32258, 34322, 37538, 38642, 44402, 45602, 49298, 53138, 55778, 59858 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 REFERENCES Pascal Ortiz, Exercices d'Algèbre, Collection CAPES / Agrégation, Ellipses, problème 1.35, pp. 70-74, 2004. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 Michael Hilgemann and Siu-Hung Ng, Hopf algebras of dimension 2p^2, arXiv:0809.0699 [math.QA], 2008. FORMULA a(n) = A079704(n+1) for n>0. EXAMPLE a(1) = 2*A065091(1)^2 = 2*3^2 = 18. a(2) = 2*A065091(2)^2 = 2*5^2 = 50. a(3) = 2*A065091(3)^2 = 2*7^2 = 98. MATHEMATICA 2#^2&/@Prime[Range[2, 40]] (* Harvey P. Dale, Jul 23 2021 *) PROG (Python) from sympy import prime def a(n): return 2*prime(n+1)**2 print([a(n) for n in range(1, 40)]) # Michael S. Branicky, Dec 10 2021 CROSSREFS Subsequence of A079704. Cf. A054397, A065091. Sequence in context: A102836 A217750 A180292 * A074173 A273459 A092068 Adjacent sequences:  A143925 A143926 A143927 * A143929 A143930 A143931 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Sep 05 2008 STATUS approved

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Last modified January 19 20:48 EST 2022. Contains 350466 sequences. (Running on oeis4.)