A355880 - OEIS

%I #11 Aug 24 2022 10:12:52

%S 0,0,0,0,0,1,1,1,1,2,2,2,2,3,3,4,4,4,4,4,4,6,6,8,8,8,8,8,8,9,9,12,12,

%T 12,12,12,12,12,12,16,16,18,18,18,18,18,18,20,20,20,20,24,24,27,27,27,

%U 27,27,27,27,27,30,30,32,32,36,36,36,36,36,36,36,36,36,36,40

%N a(n) is a maximum of t*u*v such that 2*t*u + 2*t*v + 2*u*v <= n, where t,u,v are positive integers.

%C The largest volume of a rectangular cuboid with a surface area less than or equal to n.

%o (Python)

%o for k in range(1, 200):

%o     max_v = 0

%o     for a in range(1, k):

%o         for b in range(1, a+1):

%o             for c in range(1, b+1):

%o                 if 2*a*b + 2*a*c + 2*b*c <= k and a*b*c > max_v:

%o                     max_v = a*b*c

%o     print(max_v, end = ', ')

%Y Cf. A008642.

%K nonn

%O 1,10

%A _Gleb Ivanov_, Jul 20 2022