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 A375787 #20 Nov 19 2024 00:40:47
%S A375787 0,20,17,15,8,18,4,11,5,13,1,22,2,10,13,4,1,15,1,15,9,6,0,17,3,0,1,8,
%T A375787 0,24,0,1,6,2,6,13,0,0,4,11,0,21,0,4,10,0,0,7,0,3,2,4,0,4,1,5,0,0,0,29
%N A375787 a(n) is the number of solutions of n*x*y*z = (x + n)*(y + n)*(z + n), 0 < x <= y <= z.
%C A375787 a(n) = 0 for primes n not less than 23.
%e A375787 For n=5, a(n) = 8 because 5*x*y*z = (x + 5)*(y + 5)*(z + 5), 0 < x <= y <= z has 8 integer solutions: {{2,12,595}, {2,14,95}, {2,15,70}, {2,20,35}, {3,6,220}, {3,10,20}, {4,5,45}, {5,5,20}}.
%t A375787 Table[{n, Length@Solve[n*x*y*z == (x + n) (y + n) (z + n) && 0 < x <= y <= z, {x, y, z}, Integers]}, {n, 60}][[All, 2]]
%Y A375787 Cf. A374059.
%K A375787 nonn,easy
%O A375787 1,2
%A A375787 _Zhining Yang_, Oct 28 2024