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%I #21 Dec 01 2017 18:08:04
%S 1,3,24,288,6912,165888,7962624,382205952,27518828544,1981355655168,
%T 237762678620160,22825217147535360,3834636480785940480,
%U 552187653233175429120,106020029420769682391040,20355845648787779019079680,5862483546850880357494947840
%N Product J_2(i), i=1..n.
%C a(n) is also the determinant of the symmetric n X n matrix M defined by M(i,j) = gcd(i,j)^2 for 1 <= i,j <= n. - Avi Peretz, (njk(AT)netvision.net.il), Mar 22 2001
%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 203, #17.
%H G. C. Greubel, <a href="/A059381/b059381.txt">Table of n, a(n) for n = 1..250</a>
%H Antal Bege, <a href="http://www.emis.de/journals/AUSM/C1-1/MATH1-4.PDF">Hadamard product of GCD matrices</a>, Acta Univ. Sapientiae, Mathematica, 1, 1 (2009) 43-49.
%F a(n) = A001088(n)*A175836(n). - _Enrique Pérez Herrero_, Oct 08 2011
%p f:= n-> LinearAlgebra:-Determinant(Matrix(n,n,(i,j) -> igcd(i,j)^2)):
%p map(f, [$1..40]); # _Robert Israel_, Dec 01 2017
%t JordanTotient[n_,k_:1] := DivisorSum[n,#^k*MoebiusMu[n/#]&]/;(n>0)&&IntegerQ[n]; A059381[n_]:=Times@@(JordanTotient[#,2]&/@Range[n] ); (* _Enrique Pérez Herrero_, Dec 29 2010 *)
%Y Cf. A001088, A007434, A175836.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Jan 28 2001
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