A059381 Product J_2(i), i=1..n.

1, 3, 24, 288, 6912, 165888, 7962624, 382205952, 27518828544, 1981355655168, 237762678620160, 22825217147535360, 3834636480785940480, 552187653233175429120, 106020029420769682391040, 20355845648787779019079680, 5862483546850880357494947840

Offset: 1

Author

N. J. A. Sloane, Jan 28 2001

Keywords

• nonn

Comments

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

References

• L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 203, #17.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..250
• Antal Bege, Hadamard product of GCD matrices, Acta Univ. Sapientiae, Mathematica, 1, 1 (2009) 43-49.

Crossrefs

Cf. A001088, A007434, A175836.

Programs

Maple

f:= n-> LinearAlgebra:-Determinant(Matrix(n,n,(i,j) -> igcd(i,j)^2)):
map(f, [$1..40]); # Robert Israel, Dec 01 2017

Mathematica

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 *)

Formula

a(n) = A001088(n)*A175836(n). - Enrique Pérez Herrero, Oct 08 2011