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Search: id:A140412
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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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| 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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COMMENT
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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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FORMULA
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It appears that a(n) = Product[MT2(k) * sfk(k)^2 * mu[sfk(k)), k=1,2,...,n], where MT2(k) is the kth term of the Moebius transform of the sequence of squares, sfk(k) is the square-free kernel of k and mu denotes the Moebius function.
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CROSSREFS
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Cf. A060238.
Sequence in context: A089036 A155813 A003748 this_sequence A116225 A159870 A114809
Adjacent sequences: A140409 A140410 A140411 this_sequence A140413 A140414 A140415
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KEYWORD
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sign
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Jun 17 2008
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