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A330967
a(n) is the determinant of the matrix with elements gcd(i,j) for 2 <= i,j <= n.
0
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
2,1
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.
MATHEMATICA
Table[Det[Table[GCD[i, j], {i, 2, n}, {j, 2, n}]], {n, 2, 25}]
PROG
(PARI) a(n)={matdet(matrix(n-1, n-1, i, j, gcd(i+1, j+1)))} \\ Andrew Howroyd, Jan 07 2020
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.
Sequence in context: A349449 A018451 A301520 * A139010 A018472 A082593
KEYWORD
nonn
AUTHOR
Matt Frank, Jan 04 2020
STATUS
approved