A330967 a(n) is the determinant of the matrix with elements gcd(i,j) for 2 <= i,j <= n.

2, 5, 10, 44, 104, 656, 2624, 15744, 67584, 694272, 2777088, 34062336, 213221376, 1758855168, 14070841344, 228530847744, 1371185086464, 25007480635392, 200059845083136, 2447683608379392, 25040421692375040, 556525133318062080, 4452201066544496640, 89044021330889932800

Offset: 2

Author

Matt Frank, Jan 04 2020

Keywords

• nonn

Comments

These determinants are always nonzero, as shown by Beslin and Ligh.

Links

• Scott Beslin and Steven Ligh, Greatest Common Divisor Matrices, Linear Algebra and Its Applications 119 (1989), 69-76.

Crossrefs

A001088 gives the determinants for gcd(i,j), 1 <= i,j <= n.

A067549 gives the determinants for gcd(i-th prime, j-th prime), 1 <= i,j <= n.

Programs

Mathematica

Table[Det[Table[GCD[i, j], {i, 2, n}, {j, 2, n}]], {n, 2, 25}]

PARI

a(n)={matdet(matrix(n-1, n-1, i, j, gcd(i+1,j+1)))} \\ Andrew Howroyd, Jan 07 2020