An even number n such there is not a cuboid with integer sides and surface n. more
The full list of O'Halloran numbers is :
8,
12,
20,
36,
44,
60,
84,
116,
140,
156,
204,
260,
380,
420,
660,
924.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 16 values, from 8 to 924).
n\r | 0 | 1 |
2 | 16 | 0 | 2 |
3 | 9 | 0 | 7 | 3 |
4 | 16 | 0 | 0 | 0 | 4 |
5 | 7 | 3 | 1 | 1 | 4 | 5 |
6 | 9 | 0 | 7 | 0 | 0 | 0 | 6 |
7 | 4 | 4 | 4 | 0 | 2 | 1 | 1 | 7 |
8 | 1 | 0 | 0 | 0 | 15 | 0 | 0 | 0 | 8 |
9 | 1 | 0 | 2 | 4 | 0 | 1 | 4 | 0 | 4 | 9 |
10 | 7 | 0 | 1 | 0 | 4 | 0 | 3 | 0 | 1 | 0 | 10 |
11 | 3 | 1 | 2 | 1 | 0 | 1 | 3 | 2 | 2 | 1 | 0 |
A pictorial representation of the table above
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.