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

Author

Felix Huber, Sep 17 2024

Keywords

• nonn

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.

Examples

			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.
		

Links

• Felix Huber, Table of n, a(n) for n = 1..10000
• Felix Huber, Maple programs
• Eric Weisstein's World of Mathematics, Cuboid

Crossrefs

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

Programs

Maple

See Huber link.