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%I #22 Feb 05 2021 00:21:48
%S 2,4,8,12,20,36,44,60,84,116,140,156,204,260,380,420,660,924
%N Even numbers which cannot be represented by the surface area of an n1 X n2 X n3 block.
%C Twice A025052, see there for further comments.
%F a(n) = 2 * A025052(n).
%F Surface area = 2*(n1*n2 + n1*n3 + n2*n3).
%e 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.
%o (Python)
%o from sympy import integer_nthroot
%o def aupto(lim):
%o e, r, lim2 = set(range(2, lim+1, 2)), set(), integer_nthroot(lim//2, 2)[0]
%o for n1 in range(1, lim2):
%o for n2 in range(n1, lim2):
%o for n3 in range(n2, lim+1):
%o r.add(2*(n1*n2 + n1*n3 + n2*n3))
%o return sorted(e - r)
%o print(aupto(1000)) # _Michael S. Branicky_, Feb 04 2021
%Y Cf. A025052.
%K nonn,fini
%O 1,1
%A _Andreas Boe_, Sep 05 2014
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