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A003167 Number of n-dimensional cuboids with integral edge lengths for which volume = surface area. 2
2, 10, 108, 2892, 270332 (list; graph; refs; listen; history; text; internal format)
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

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

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.

For n=4 see the Marcus link.

CROSSREFS

Sequence in context: A185396 A003222 A262145 * 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) and examples from Joseph Myers, Feb 24 2004

STATUS

approved

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Last modified March 22 22:05 EDT 2017. Contains 283901 sequences.