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 A374059 #41 Dec 04 2024 09:12:41
%S A374059 1,11,13,25,7,9,22,48,5,21,14,8,280,10,1020,4,70,3,6,240,2,42,12,660,
%T A374059 30
%N A374059 a(n) is the smallest integer k such that k*x*y*z = (x + k) * (y + k) * (z + k), 0 < x <= y <= z has exactly n integer solutions.
%C A374059 a(27)=630, a(29)=60, a(30)=420. No solutions were found for n={25,26,28} with k<10^5.
%e A374059 For n=8, a(n)=5 because 5 is the smallest integer such that 5*x*y*z = (x+5)*(y+5)*(z+5), 0 < x <= y <= z has exactly 8 positive 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}}.
%Y A374059 Cf. A375787.
%K A374059 nonn,more
%O A374059 0,2
%A A374059 _Zhining Yang_, Oct 28 2024
%E A374059 a(12) corrected by _Jinyuan Wang_, Dec 04 2024