%I A003167
%S A003167 2,10,108,2892,270332
%N A003167 Number of n-dimensional cuboids with integral edge lengths for which 
               volume = surface area.
%C A003167 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 (jvospost3(AT)gmail.com), Mar 15 2006
%D A003167 Gannon, Bonsangue and Redfern, Math. Teacher, 90 (#3, 1997), pp. 188-191.
%e A003167 For n=2 the cuboids are 3 X 6 and 4 X 4.
%e A003167 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.
%e A003167 For n=4 the cuboids are: 3 X 7 X 43 X 1806, 3 X 7 X 44 X 924, 3 X 7 X 
               45 X 630, 3 X 7 X 46 X 483, 3 X 7 X 48 X 336, 3 X 7 X 49 X 294,
%e A003167 3 X 7 X 51 X 238, 3 X 7 X 54 X 189, 3 X 7 X 56 X 168, 3 X 7 X 60 X 140, 
               3 X 7 X 63 X 126, 3 X 7 X 70 X 105, 3 X 7 X 78 X 91, 3 X 7 X 84 X 
               84,
%e A003167 3 X 8 X 25 X 600, 3 X 8 X 26 X 312, 3 X 8 X 27 X 216, 3 X 8 X 28 X 168, 
               3 X 8 X 30 X 120, 3 X 8 X 32 X 96, 3 X 8 X 33 X 88, 3 X 8 X 36 X 
               72,
%e A003167 3 X 8 X 40 X 60, 3 X 8 X 42 X 56, 3 X 8 X 48 X 48, 3 X 9 X 19 X 342, 
               3 X 9 X 20 X 180, 3 X 9 X 21 X 126, 3 X 9 X 22 X 99, 3 X 9 X 24 X 
               72,
%e A003167 3 X 9 X 27 X 54, 3 X 9 X 30 X 45, 3 X 9 X 36 X 36, 3 X 10 X 16 X 240, 
               3 X 10 X 18 X 90, 3 X 10 X 20 X 60, 3 X 10 X 24 X 40, 3 X 10 X 30 
               X 30,
%e A003167 3 X 11 X 14 X 231, 3 X 11 X 15 X 110, 3 X 11 X 22 X 33, 3 X 12 X 13 X 
               156, 3 X 12 X 14 X 84, 3 X 12 X 15 X 60, 3 X 12 X 16 X 48, 3 X 12 
               X 18 X 36,
%e A003167 3 X 12 X 20 X 30, 3 X 12 X 21 X 28, 3 X 12 X 24 X 24, 3 X 13 X 13 X 78, 
               3 X 14 X 14 X 42, 3 X 14 X 15 X 35, 3 X 14 X 21 X 21, 3 X 15 X 15 
               X 30,
%e A003167 3 X 15 X 20 X 20, 3 X 16 X 16 X 24, 3 X 18 X 18 X 18, 4 X 5 X 21 X 420, 
               4 X 5 X 22 X 220, 4 X 5 X 24 X 120, 4 X 5 X 25 X 100, 4 X 5 X 28 
               X 70,
%e A003167 4 X 5 X 30 X 60, 4 X 5 X 36 X 45, 4 X 5 X 40 X 40, 4 X 6 X 13 X 156, 
               4 X 6 X 14 X 84, 4 X 6 X 15 X 60, 4 X 6 X 16 X 48, 4 X 6 X 18 X 36,
%e A003167 4 X 6 X 20 X 30, 4 X 6 X 21 X 28, 4 X 6 X 24 X 24, 4 X 7 X 10 X 140, 
               4 X 7 X 12 X 42, 4 X 7 X 14 X 28, 4 X 8 X 9 X 72, 4 X 8 X 10 X 40,
%e A003167 4 X 8 X 12 X 24, 4 X 8 X 16 X 16, 4 X 9 X 9 X 36, 4 X 9 X 12 X 18, 4 
               X 10 X 10 X 20, 4 X 10 X 12 X 15, 4 X 12 X 12 X 12, 5 X 5 X 11 X 
               110,
%e A003167 5 X 5 X 12 X 60, 5 X 5 X 14 X 35, 5 X 5 X 15 X 30, 5 X 5 X 20 X 20, 5 
               X 6 X 8 X 120, 5 X 6 X 9 X 45, 5 X 6 X 10 X 30, 5 X 6 X 12 X 20,
%e A003167 5 X 6 X 15 X 15, 5 X 7 X 7 X 70, 5 X 8 X 8 X 20, 5 X 10 X 10 X 10, 6 
               X 6 X 7 X 42, 6 X 6 X 8 X 24, 6 X 6 X 9 X 18, 6 X 6 X 10 X 15,
%e A003167 6 X 6 X 12 X 12, 6 X 7 X 7 X 21, 6 X 8 X 8 X 12, 6 X 9 X 9 X 9, 7 X 7 
               X 7 X 14, 8 X 8 X 8 X 8.
%Y A003167 Sequence in context: A049538 A127728 A003222 this_sequence A062412 A006608 
               A066205
%Y A003167 Adjacent sequences: A003164 A003165 A003166 this_sequence A003168 A003169 
               A003170
%K A003167 nonn,hard
%O A003167 2,1
%A A003167 mjzerger(AT)adams.edu
%E A003167 a(5), a(6) and examples from Joseph Myers (jsm(AT)polyomino.org.uk), 
               Feb 24 2004