A375786 a(n) is the minimum volume of an integer-sided cuboid having the same surface as a cube with edge length n.

1, 8, 13, 36, 37, 104, 73, 188, 121, 252, 181, 428, 253, 540, 337, 764, 433, 828, 541, 1196, 661, 1448, 793, 1476, 937, 2024, 1093, 2160, 1261, 2592, 1441, 2628, 1633, 3464, 1837, 3884, 2053, 3708, 2281, 4796, 2521, 5148, 2773, 5616, 3037, 5436, 3313, 6660, 3601

Offset

1,2

Comments

Conjecture: From the integer-sided cuboids with same surface 6*n^2 always the one with the smallest edge length has the minimum volume. If there are several integer-sided cuboids having the smallest edge length, then the one with the smallest second smallest edge length has the minimum volume (checked up to a(1000)).

The maximum volume is always A000578(n) = n^3.

Links

Felix Huber, Table of n, a(n) for n = 1..10000

Felix Huber, Maple programs

Eric Weisstein's World of Mathematics, Cuboid

Example

a(6) = 104: because from the five integer-sided cuboids (2, 2, 26), (2, 5, 14), (2, 6, 12), (3, 6, 10), (6, 6, 6) having the same surface as a cube with edge length 6 (see example in A375785) has (2, 2, 26) with 2*2*26 = 104 the smallest volume.

Maple

See Huber link.

Crossrefs

Cf. A000578, A369951, A375580, A375785.

Sequence in context: A063585 A258768 A048851 * A039298 A360790 A218627

Adjacent sequences: A375783 A375784 A375785 * A375787 A375788 A375789

Keyword

nonn

Author

Felix Huber, Sep 17 2024

Status

approved