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 A375786 #6 Sep 20 2024 06:43:53 %S A375786 1,8,13,36,37,104,73,188,121,252,181,428,253,540,337,764,433,828,541, %T A375786 1196,661,1448,793,1476,937,2024,1093,2160,1261,2592,1441,2628,1633, %U A375786 3464,1837,3884,2053,3708,2281,4796,2521,5148,2773,5616,3037,5436,3313,6660,3601 %N A375786 a(n) is the minimum volume of an integer-sided cuboid having the same surface as a cube with edge length n. %C A375786 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)). %C A375786 The maximum volume is always A000578(n) = n^3. %H A375786 Felix Huber, <a href="/A375786/b375786.txt">Table of n, a(n) for n = 1..10000</a> %H A375786 Felix Huber, <a href="/A375786/a375786.txt">Maple programs</a> %H A375786 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Cuboid.html">Cuboid</a> %e A375786 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. %p A375786 See Huber link. %Y A375786 Cf. A000578, A369951, A375580, A375785. %K A375786 nonn %O A375786 1,2 %A A375786 _Felix Huber_, Sep 17 2024