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A059383 Product J_4(i), i=1..n. 7

%I

%S 1,15,1200,288000,179712000,215654400000,517570560000000,

%T 1987470950400000000,12878811758592000000000,

%U 120545678060421120000000000,1764788726804565196800000000000,33883943554647651778560000000000000,967725427920736934795673600000000000000

%N Product J_4(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)^4 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="/A059383/b059383.txt">Table of n, a(n) for n = 1..140</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]; A059383[n_]:=Times@@(JordanTotient[#, 4]&/@Range[n]); (* _Enrique PĂ©rez Herrero_, Aug 12 2011 *)

%Y Cf. A001088, A059377, A059381, A059382, A059383, A059384, A175836.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Jan 28 2001

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Last modified April 9 06:25 EDT 2020. Contains 333343 sequences. (Running on oeis4.)