A120294 Numerator of determinant of n X n matrix with elements M[j,j] = (i+j)/(i+j-1).

2, 5, 1, 17, 13, 37, 1, 1, 41, 101, 61, 29, 1, 197, 113, 257, 1, 1, 181, 401, 1, 97, 53, 577, 313, 677, 73, 157, 421, 1, 1, 1, 109, 89, 613, 1297, 137, 1, 761, 1601

Offset: 1

Author

Alexander Adamchuk, Jul 10 2006

Keywords

• frac
• nonn

Comments

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.

Crossrefs

Cf. A005249, A002312, A005528, A005529, A002522.

Programs

Mathematica

Numerator[Table[Det[Table[(i+j)/(i+j-1),{i,1,n},{j,1,n}]],{n,1,40}]]

Formula

a(n) = numerator[Det[Table[(i+j)/(i+j-1),{i,1,n},{j,1,n}]]].