

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 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

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



