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A060239 det(P*Q)/n! where P, Q are n X n matrices with P[i,j]=lcm(i,j), Q[i,j]=gcd(i,j). 3

%I

%S 1,-1,4,-8,128,512,-18432,73728,-884736,-14155776,1415577600,

%T 11324620800,-1630745395200,-58706834227200,-3757237390540800,

%U 30057899124326400,-7694822175827558400,-92337866109930700800

%N det(P*Q)/n! where P, Q are n X n matrices with P[i,j]=lcm(i,j), Q[i,j]=gcd(i,j).

%H Enrique PĂ©rez Herrero, <a href="/A060239/b060239.txt">Table of n, a(n) for n = 1..100</a>

%F a(n)=A001088(n)*A060238(n)/n!

%o (Sage)

%o def A060239(n):

%o ....P = Matrix(lambda i,j: lcm(i+1,j+1), nrows=n)

%o ....Q = Matrix(lambda i,j: gcd(i+1,j+1), nrows=n)

%o ....return (P*Q).det()/factorial(n) # [D. S. McNeil, Jan 16 2011]

%Y Cf. A001088, A060238.

%K sign

%O 1,3

%A MCKAY john (mckay(AT)cs.concordia.ca), Mar 21 2001

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Last modified November 19 11:09 EST 2019. Contains 329319 sequences. (Running on oeis4.)