A246850 Even numbers which cannot be represented by the surface area of an n1 X n2 X n3 block.

2, 4, 8, 12, 20, 36, 44, 60, 84, 116, 140, 156, 204, 260, 380, 420, 660, 924

Offset: 1

Author

Andreas Boe, Sep 05 2014

Keywords

• nonn
• fini

Comments

Twice A025052, see there for further comments.

Examples

			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.
		

Crossrefs

Cf. A025052.

Programs

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)
print(aupto(1000)) # Michael S. Branicky, Feb 04 2021

Formula

a(n) = 2 * A025052(n).

Surface area = 2*(n1*n2 + n1*n3 + n2*n3).