This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A375785 #7 Sep 20 2024 06:43:41 %S A375785 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, %T A375785 23,21,41,21,31,35,29,33,45,25,29,35,51,29,41,29,45,61,39,33,61,33,57, %U A375785 51,45,37,63,61,51,51,49,41,97,41,49,61,63,61,81,45,67,67 %N A375785 a(n) is the number of distinct integer-sided cuboids having the same surface as a cube with edge length n. %C A375785 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. %C A375785 Conjecture: All terms are odd. %H A375785 Felix Huber, <a href="/A375785/b375785.txt">Table of n, a(n) for n = 1..10000</a> %H A375785 Felix Huber, <a href="/A375785/a375785.txt">Maple programs</a> %H A375785 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Cuboid.html">Cuboid</a> %e A375785 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. %p A375785 See Huber link. %Y A375785 Cf. A000578, A003167, A066955, A369951, A375580, A375786, A376074. %K A375785 nonn %O A375785 1,3 %A A375785 _Felix Huber_, Sep 17 2024