A007361 - OEIS

%I M3201 #24 Aug 24 2023 10:32:48

%S 1,4,2,4,8,64,64,256

%N Numerator of n-th power of Hermite constant for dimension n.

%C From the work of Cohn and Kumar we know that a(24) = 4^24 = 281474976710656.

%D Iskander Aliev, On the lattice programming gap of the group problems, Operations Research Letters 43 (2015) 199-202

%D J. W. S. Cassels, An Introduction to the Geometry of Numbers. Springer-Verlag, NY, 2nd ed., 1971, p. 332.

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 20.

%D P. M. Gruber and C. G. Lekkerkerker, Geometry of Numbers, North-Holland, Amsterdam, 2nd ed., 1987, p. 410.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H H. Cohn and A. Kumar, <a href="https://arxiv.org/abs/math/0403263">Optimality and uniqueness of the Leech lattice among lattices</a>, arXiv:math/0403263 [math.MG], 2004-2017.

%H H. Cohn and A. Kumar, <a href="https://arxiv.org/abs/math/0408174">The densest lattice in twenty-four dimensions</a>, arXiv:math/0408174 [math.MG], 2004.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HermiteConstants.html">Hermite Constants.</a>

%e 1, 4/3, 2, 4, 8, 64/3, 64, 256, ... = A007361/A007362.

%Y Cf. A007362.

%K nonn,hard,nice,frac

%O 1,2

%A _N. J. A. Sloane_