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%I #18 Jan 09 2020 03:27:51
%S 2,5,10,44,104,656,2624,15744,67584,694272,2777088,34062336,213221376,
%T 1758855168,14070841344,228530847744,1371185086464,25007480635392,
%U 200059845083136,2447683608379392,25040421692375040,556525133318062080,4452201066544496640,89044021330889932800
%N a(n) is the determinant of the matrix with elements gcd(i,j) for 2 <= i,j <= n.
%C These determinants are always nonzero, as shown by Beslin and Ligh.
%H Scott Beslin and Steven Ligh, <a href="https://doi.org/10.1016/0024-3795(89)90572-7">Greatest Common Divisor Matrices</a>, Linear Algebra and Its Applications 119 (1989), 69-76.
%t Table[Det[Table[GCD[i, j], {i, 2, n}, {j, 2, n}]], {n, 2, 25}]
%o (PARI) a(n)={matdet(matrix(n-1, n-1, i, j, gcd(i+1,j+1)))} \\ _Andrew Howroyd_, Jan 07 2020
%Y A001088 gives the determinants for gcd(i,j), 1 <= i,j <= n.
%Y A067549 gives the determinants for gcd(i-th prime, j-th prime), 1 <= i,j <= n.
%K nonn
%O 2,1
%A _Matt Frank_, Jan 04 2020