%I #7 Mar 25 2014 07:03:00
%S 1,63,45864,184923648,2889247076352,132512427909808128,
%T 15589822118733106642944,4022922418094840702998413312,
%U 2135013202351949099169693925638144,2101519115233451721701919767332732796928,3722967203782973732098252983015976113725767680
%N Product_{i=1..n} J_6(i) where J_6(i) = A069091(i).
%C This is the generalized factorial for A069091.
%C a(n) is also the determinant of the symmetric n X n matrix M defined by M(i,j) = gcd(i,j)^6 for 1 <= i,j <= n.
%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 203, #17.
%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>
%o (Sage)
%o q=15 # change q for more terms
%o J6=[i^6*prod([1-1/p^6 for p in prime_divisors(i)]) for i in [1..q]]
%o [prod(J6[0:i+1]) for i in [0..q-1]]
%Y Cf. A069091, A175836, A059381, A059382, A059383.
%K nonn
%O 1,2
%A _Tom Edgar_, Mar 23 2014