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%I #13 Mar 04 2018 16:52:09
%S 1,-12,864,-41472,24883200,21499084800,-50565847449600,
%T 9708642710323200,-6291200476289433600,-45296643429283921920000,
%U 657707262593202546278400000,2273036299522107999938150400000,-64536046616031690334243966156800000
%N Determinants of the n X n matrices whose (i,j)-elements are lcm(i^2, j^2).
%C The determinants of the n X n matrices whose (i,j)-elements are lcm(i,j) are given in A060238.
%F 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.
%o (PARI) a(n) = matdet(matrix(n, n, i, j, lcm(i^2, j^2))); \\ _Michel Marcus_, Jul 10 2014
%Y Cf. A060238.
%K sign
%O 1,2
%A _John W. Layman_, Jun 17 2008