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 A239620 #17 Feb 16 2025 08:33:21 %S A239620 0,0,10,151,1714,17873,180953,1815841,18174211 %N A239620 Number of Euler bricks with side length a < b < c < 10^n, i.e., in a boxed parameter space with dimension 10^n. %C A239620 An Euler brick is a cuboid of integer side dimensions a, b, c such that the face diagonals are integers. %C A239620 Because the sides of a cuboid are permutable without changing its shape, the total number of Euler bricks in the parameter space is b(n) = 6*a(n) = 0, 0, 60, 906, 10284, ... %H A239620 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EulerBrick.html">Euler Brick</a> %H A239620 <a href="/index/Br#bricks">Index entries for sequences related to bricks</a> %e A239620 a(3) = 10, since there are the ten Euler bricks [44, 117, 240], [85, 132, 720], [88, 234, 480], [132, 351, 720], [140, 480, 693], [160, 231, 792], [176, 468, 960], [240, 252, 275], [480, 504, 550], [720, 756, 825] with longest side length < 1000. %o A239620 (Sage) %o A239620 def a(n): %o A239620 ans = 0 %o A239620 for x in range(1,10^n): %o A239620 divs = Integer(x^2).divisors() %o A239620 for d in divs: %o A239620 if (d <= x^2/d): continue %o A239620 if (d-x^2/d >= 2*x): break %o A239620 if (d-x^2/d)%2==0: %o A239620 y = (d-x^2/d)/2 %o A239620 for e in divs: %o A239620 if (e <= x^2/e): continue %o A239620 if (e-x^2/e >= 2*y): break %o A239620 if (e-x^2/e)%2==0: %o A239620 z = (e-x^2/e)/2 %o A239620 if (y^2+z^2).is_square(): %o A239620 ans += 1 %o A239620 return ans # _Robin Visser_, Jan 01 2024 %Y A239620 Cf. A031173, A031174, A031175, A239618. %K A239620 nonn,more %O A239620 1,3 %A A239620 _Martin Renner_, Mar 22 2014 %E A239620 a(6)-a(8) from _Giovanni Resta_, Mar 22 2014 %E A239620 a(9) from _Robin Visser_, Jan 01 2024