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 A291420 #44 Nov 05 2021 17:30:55 %S A291420 341880,8168160,14636160,17957940,52492440,116396280,1071572040, %T A291420 1187525640,1728483120,5988702720,6609482880,22539095040,29239970760, %U A291420 136496680320,258670630680,398648544840,494892478080,592003418160,1329673884000,1343798407560,2190884461920 %N A291420 Numbers n such that there exist exactly four distinct Pythagorean triangles, at least one of them primitive, with area n. %C A291420 Numbers n such that there exist positive integers x, y with x > y and n = x*y*(x-y)*(x+y). %C A291420 Many of them consist of a Pythagorean triangle plus a triple which is a solution to Carroll's problem: Find three Pythagorean triangles with the same area. %e A291420 p^2 - p*q + q^2 = r^2; %e A291420 p = 208, q = 418, r = 362, q - p = 210; %e A291420 n = p*r*q*(q-p) = 208*418*362*210 = 6609482880. %e A291420 x = 640, y = 627 gives the same area: %e A291420 n = x*y*(x-y)*(x+y) = 640*627*13*1267 = 6609482880. %Y A291420 Cf. A009127, A024407, A055193, A088513, A088977, A089025, A177021, A291591. %K A291420 nonn %O A291420 1,1 %A A291420 _Sture Sjöstedt_, Aug 23 2017 %E A291420 a(12)-a(21) from _Giovanni Resta_, Aug 28 2017