A375785 a(n) is the number of distinct integer-sided cuboids having the same surface as a cube with edge length n.

1, 1, 3, 3, 5, 5, 5, 7, 9, 9, 9, 13, 9, 9, 19, 15, 13, 19, 13, 23, 19, 19, 17, 29, 25, 19, 27, 23, 21, 41, 21, 31, 35, 29, 33, 45, 25, 29, 35, 51, 29, 41, 29, 45, 61, 39, 33, 61, 33, 57, 51, 45, 37, 63, 61, 51, 51, 49, 41, 97, 41, 49, 61, 63, 61, 81, 45, 67, 67

Offset

1,3

Comments

a(n) is the number of unordered solutions (x, y, z) to x*y + y*z + x*z = 3*n^2 in positive integers x and y.

Conjecture: All terms are odd.

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) = 5 because exactly the 5 integer-sided cuboids (2, 2, 26), (2, 5, 14), (2, 6, 12), (3, 6, 10), (6, 6, 6) have the same surface as a cube with edge length 6: 2*(2*2 + 2*26 + 2*26) = 2*(2*5 + 5*14 + 2*14) = 2*(2*6 + 6*12 + 2*12) = 2*(3*6 + 6*10 + 3*10) = 2*(6*6 + 6*6 + 6*6) = 6*6^2.

Maple

See Huber link.

Crossrefs

Cf. A000578, A003167, A066955, A369951, A375580, A375786, A376074.

Sequence in context: A203998 A257371 A075260 * A054847 A335266 A067782

Adjacent sequences: A375782 A375783 A375784 * A375786 A375787 A375788

Keyword

nonn

Author

Felix Huber, Sep 17 2024

Status

approved