A007362 - OEIS

A007362

Denominator of n-th power of Hermite constant for dimension n.
(Formerly M2209)

1, 3, 1, 1, 1, 3, 1, 1

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OFFSET

1,2

COMMENTS

From the work of Cohn and Kumar we know that a(24) = 1.

REFERENCES

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

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

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

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

LINKS

H. Cohn and A. Kumar, Optimality and uniqueness of the Leech lattice among lattices, arXiv:math/0403263 [math.MG], 2004-2017.

H. Cohn and A. Kumar, The densest lattice in twenty-four dimensions, arXiv:math/0408174 [math.MG], 2004.

Eric Weisstein's World of Mathematics, Hermite Constants.

EXAMPLE

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

CROSSREFS

KEYWORD

nonn,hard,nice,frac,changed

AUTHOR

STATUS

approved