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A140412
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Determinants of the n X n matrices whose (i,j)-elements are lcm(i^2, j^2).
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0
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1, -12, 864, -41472, 24883200, 21499084800, -50565847449600, 9708642710323200, -6291200476289433600, -45296643429283921920000, 657707262593202546278400000, 2273036299522107999938150400000, -64536046616031690334243966156800000
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OFFSET
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1,2
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COMMENTS
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The determinants of the n X n matrices whose (i,j)-elements are lcm(i,j) are given in A060238.
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LINKS
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FORMULA
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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.
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PROG
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(PARI) a(n) = matdet(matrix(n, n, i, j, lcm(i^2, j^2))); \\ Michel Marcus, Jul 10 2014
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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