A003167 Number of n-dimensional cuboids with integral edge lengths for which volume = surface area.

2, 10, 108, 2892, 270332

Offset

2,1

Comments

For n>1 it is always true that a(n) > 0 because for dimension n we always have the n-dimensional cuboid with all edge lengths = 2n = A062971(n) having hypervolume (2n)^n equal to "surface hyper-area". - Jonathan Vos Post, Mar 15 2006

Number of nondecreasing tuples (x_1, x_2, ..., x_n) such that 1/2 = 1/x_1 + 1/x_2 + ... + 1/x_n. - Lewis Chen, Dec 20 2019

Links

Table of n, a(n) for n=2..6.

Gerald E. Gannon, Martin V. Bonsangue and Terrence J. Redfern, One Good Problem Leads to Another and Another and..., Math. Teacher, 90 (#3, 1997), pp. 188-191.

Michel Marcus, Cuboids for n=4, after Joseph Myers.

Example

From Joseph Myers, Feb 24 2004: (Start)
For n=2 the cuboids are 3 X 6 and 4 X 4.
For n=3 the cuboids are 3 X 7 X 42, 3 X 8 X 24, 3 X 9 X 18, 3 X 10 X 15, 3 X 12 X 12, 4 X 5 X 20, 4 X 6 X 12, 4 X 8 X 8, 5 X 5 X 10, 6 X 6 X 6. (End)
For n=4 see the Marcus link.

Crossrefs

Cf. A002966.

Sequence in context: A262145 A355209 A343307 * A240625 A062412 A212491

Adjacent sequences: A003164 A003165 A003166 * A003168 A003169 A003170

Keyword

nonn,hard,more

Author

mjzerger(AT)adams.edu

Extensions

a(5)-a(6) from Joseph Myers, Feb 24 2004

Status

approved