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%I #24 Jun 01 2022 09:43:19
%S 1,31,7502,7441984,23248758016,174412182636032,2931171141381153792,
%T 93047096712003345973248,5471727569246068763302821888,
%U 529903984716066283313298482921472,85341036738522474927606720674503065600,20487310643596659421020979792003903940198400
%N a(n) = Product_{i=1..n} J_5(i).
%C a(n) is also the determinant of the symmetric n X n matrix M defined by M(i,j) = gcd(i,j)^5 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="/A059384/b059384.txt">Table of n, a(n) for n = 1..120</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_Integer, k_: 1] := DivisorSum[n, #^k*MoebiusMu[n/#] &]; f[n_] := Times @@ (JordanTotient[#, 5] & /@ Range[n]); (* _Enrique Pérez Herrero_ *) Array[f, 11] (* _Robert G. Wilson v_, Oct 08 2011 *)
%Y Cf. A001088, A059378, A059381, A059382, A059383, A175836.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Jan 28 2001
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