A143928 2*p^2, for p an odd prime.

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

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 * A356743 A074173 A273459

Adjacent sequences: A143925 A143926 A143927 * A143929 A143930 A143931

Keyword

easy,nonn

Author

Jonathan Vos Post, Sep 05 2008

Status

approved