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
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
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Sep 05 2008
STATUS
approved