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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..13.

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.

PROG

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

CROSSREFS

Cf. A060238.

Sequence in context: A203410 A275568 A271433 * A276013 A116225 A214313

Adjacent sequences:  A140409 A140410 A140411 * A140413 A140414 A140415

KEYWORD

sign

AUTHOR

John W. Layman, Jun 17 2008

STATUS

approved

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Last modified September 22 16:22 EDT 2020. Contains 337291 sequences. (Running on oeis4.)