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A059381 Product J_2(i), i=1..n. 9
1, 3, 24, 288, 6912, 165888, 7962624, 382205952, 27518828544, 1981355655168, 237762678620160, 22825217147535360, 3834636480785940480, 552187653233175429120, 106020029420769682391040, 20355845648787779019079680, 5862483546850880357494947840 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

FORMULA

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

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 *)

CROSSREFS

Cf. A001088, A007434, A175836.

Sequence in context: A257453 A128572 A052592 * A301933 A292186 A258301

Adjacent sequences:  A059378 A059379 A059380 * A059382 A059383 A059384

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 28 2001

STATUS

approved

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Last modified November 21 11:32 EST 2018. Contains 317447 sequences. (Running on oeis4.)