A355880 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.

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, 12, 12, 12, 12, 12, 12, 16, 16, 18, 18, 18, 18, 18, 18, 20, 20, 20, 20, 24, 24, 27, 27, 27, 27, 27, 27, 27, 27, 30, 30, 32, 32, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 40

Offset

1,10

Comments

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

Links

Table of n, a(n) for n=1..76.

Prog

(Python)
for k in range(1, 200):
    max_v = 0
    for a in range(1, k):
        for b in range(1, a+1):
            for c in range(1, b+1):
                if 2*a*b + 2*a*c + 2*b*c <= k and a*b*c > max_v:
                    max_v = a*b*c
    print(max_v, end = ', ')

Crossrefs

Cf. A008642.

Sequence in context: A364678 A175387 A024542 * A209082 A257684 A098424

Adjacent sequences: A355877 A355878 A355879 * A355881 A355882 A355883

Keyword

nonn

Author

Gleb Ivanov, Jul 20 2022

Status

approved