A140412 Determinants of the n X n matrices whose (i,j)-elements are lcm(i^2, j^2).

1, -12, 864, -41472, 24883200, 21499084800, -50565847449600, 9708642710323200, -6291200476289433600, -45296643429283921920000, 657707262593202546278400000, 2273036299522107999938150400000, -64536046616031690334243966156800000

Offset: 1

Author

John W. Layman, Jun 17 2008

Keywords

• sign

Comments

The determinants of the n X n matrices whose (i,j)-elements are lcm(i,j) are given in A060238.

Crossrefs

Cf. A060238.

Programs

PARI

a(n) = matdet(matrix(n, n, i, j, lcm(i^2, j^2))); \\ Michel Marcus, Jul 10 2014

Formula

It appears that a(n) = Product_{k=1..n} MT2(k) * rad(k)^2 * mu(rad(k)), where MT2(k) is the k-th term of the Moebius transform of the sequence of squares, rad(k) is the squarefree kernel of k and mu denotes the Moebius function.