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 A120294 #6 Aug 06 2025 01:03:22
%S A120294 2,5,1,17,13,37,1,1,41,101,61,29,1,197,113,257,1,1,181,401,1,97,53,
%T A120294 577,313,677,73,157,421,1,1,1,109,89,613,1297,137,1,761,1601
%N A120294 Numerator of determinant of n X n matrix with elements M[j,j] = (i+j)/(i+j-1).
%C A120294 Some a(n) are equal to 1 (for n=3,7,8,13,17,18,21,30,31,32,38..=A002312 Arc-cotangent reducible numbers or non-Stormer numbers). All other a(n) (for n=1,2,4,5,6,9,10,11,14,15,16,19,20,22,23..=A005528 Stormer numbers or arc-cotangent irreducible numbers, largest prime factor of n^2 + 1 is >= 2n.) belong to A005529 - Primitive prime factors of the sequence k^2 + 1 (A002522) in the order that they are found. Matrix M[i,j] = (i+j)/(i+j-1) = 1 + 1/(i+j-1) is a sum of n X n unit matrix and n X n Hilbert Matrix. Denominator of determinant of matrix M[i,j] equals determinant of inverse Hilbert matrix A005249.
%F A120294 a(n) = numerator[Det[Table[(i+j)/(i+j-1),{i,1,n},{j,1,n}]]].
%t A120294 Numerator[Table[Det[Table[(i+j)/(i+j-1),{i,1,n},{j,1,n}]],{n,1,40}]]
%Y A120294 Cf. A005249, A002312, A005528, A005529, A002522.
%K A120294 frac,nonn
%O A120294 1,1
%A A120294 _Alexander Adamchuk_, Jul 10 2006