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Determinant of the n X n matrix with entries gcd(X,Y)^gcd(X,Y).
0

%I #2 Mar 31 2012 13:21:57

%S 1,1,3,78,19656,61405344,2863085569344,2357871215948696448,

%T 39557911075122642360238080,15325544184478930809864207383592960,

%U 153255393906487099048546500580688904121221120

%N Determinant of the n X n matrix with entries gcd(X,Y)^gcd(X,Y).

%e for n = 3:

%e [1,1,1]

%e [1,4,1]

%e [1,1,27]

%e with det 78.

%o (PARI) for(i=0,10,m=matrix(i,i,X,Y,gcd(X,Y)^gcd(X,Y));print1(","matdet(m)))

%Y Cf. A000178:super-factorials, A001088:product(A000010(i)).

%K nonn

%O 0,3

%A _Jon Perry_, Mar 22 2004