

A140412


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


0



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

1,2


COMMENTS

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


LINKS



FORMULA

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


PROG

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


CROSSREFS



KEYWORD

sign


AUTHOR



STATUS

approved



