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 A381644 #5 Mar 11 2025 15:50:47
%S A381644 0,21313,35472,28901,36366,35534,33048,55548,30891,60741,76106,161909,
%T A381644 88494,114437,220621,76856,56832,195942,33510,212618,222606,154046,
%U A381644 21700,324700,107022,94149,109693,244884,35992,592482,39051,134282,213723,104829,363935,355519,70334,110560,158300,485946,46982,650655
%N A381644 a(n) is the number of positive integer solutions of n*x*y*z*v*w = (x + n) * (y + n) * (z + n) * (v + n) * (w + n), x <= y <= z <= v <= w.
%e A381644 For n=4, a(4) = 28901 because 4*x*y*z*v*w = (x + 4)*(y + 4)*(z + 4)*(v + 4)*(w + 4), 0 < x <= y <= z <= v <= w has 28901 positive integer solutions: {{2,13,205,42637,1818041676},{2,13,205,42638,909042156},{2,13,205,42639,606042316},{2,13,205,42640,454542396}, ..., {10, 10, 12, 14, 21}, {10, 11, 12, 14, 18}, {10, 12, 12, 14, 16}}.
%t A381644 Table[Length@Solve[n*x*y*z*v*w == (x + n) (y + n) (z + n) (v + n) (w + n) &&
%t A381644 0 < x <= y <= z <= v <= w, {x, y, z, v, w}, Integers], {n, 8}]
%Y A381644 Cf. A374059, A375787, A380749, A380750.
%K A381644 nonn
%O A381644 1,2
%A A381644 _Zhining Yang_, Mar 03 2025