

A003167


Number of ndimensional cuboids with integral edge lengths for which volume = surface area.


2




OFFSET

2,1


COMMENTS

For n>1 it is always true that a(n) > 0 because for dimension n we always have the ndimensional cuboid with all edge lengths = 2n = A062971(n) having hypervolume (2n)^n equal to "surface hyperarea".  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. 188191.
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: 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) from Joseph Myers, Feb 24 2004


STATUS

approved



