|
|
A246850
|
|
Even numbers which cannot be represented by the surface area of an n1 X n2 X n3 block.
|
|
0
|
|
|
2, 4, 8, 12, 20, 36, 44, 60, 84, 116, 140, 156, 204, 260, 380, 420, 660, 924
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Twice A025052, see there for further comments.
|
|
LINKS
|
|
|
FORMULA
|
Surface area = 2*(n1*n2 + n1*n3 + n2*n3).
|
|
EXAMPLE
|
A 1 X 1 X 1 block has surface area 6. A 1 X 1 X 2 block has surface area 10. No n1 X n2 X n3 block of intermediate size exists, so there is no way to create an n1 X n2 X n3 block with surface area 8.
|
|
PROG
|
(Python)
from sympy import integer_nthroot
def aupto(lim):
e, r, lim2 = set(range(2, lim+1, 2)), set(), integer_nthroot(lim//2, 2)[0]
for n1 in range(1, lim2):
for n2 in range(n1, lim2):
for n3 in range(n2, lim+1):
r.add(2*(n1*n2 + n1*n3 + n2*n3))
return sorted(e - r)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,fini
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|