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%I #13 Apr 17 2015 08:04:43
%S 1,7,182,10192,1263808,230013056,78664465152,35241680388096,
%T 24739659632443392,21474024560960864256,28560452666077949460480,
%U 41584019081809494414458880,91318505903653649734151700480,218616503133346837463559170949120
%N Product J_3(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)^3 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 Enrique Pérez Herrero, <a href="/A059382/b059382.txt">Table of n, a(n) for n = 1..100</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.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LePaigesTheorem.html">Le Paige's Theorem</a>
%t JordanTotient[n_, k_:1]:=DivisorSum[n, #^k*MoebiusMu[n/#]&]/; (n>0)&&IntegerQ[n]; A059382[n_]:=Times@@(JordanTotient[#, 3]&/@Range[n]); (* _Enrique Pérez Herrero_, Aug 06 2011 *)
%Y Cf. A001088, A059376, A059381, A059383, A059384, A175836.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Jan 28 2001
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