A177066 - OEIS

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A177066

Determinant of the symmetric n X n matrix M defined by M(i,j) = gcd(2i-1,2j-1) for 1 <= i,j <= n.

1, 2, 8, 48, 288, 2880, 34560, 276480, 4423680, 79626240, 955514880, 21021327360, 420426547200, 7567677849600, 211894979788800, 6356849393664000, 127136987873280000, 3051287708958720000, 109846357522513920000

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OFFSET

1,2

COMMENTS

It appears, but has not been proved, that the ratios a(n+1)/a(n) give phi(2n+1) (A037225).

See A001088, A059381, and A059382 for determinants of matrices M defined by M(i,j) = gcd(i,j), gcd(i^2,j^2), and gcd(i^3,j^3), respectively.

LINKS

Table of n, a(n) for n=1..19.

MAPLE

A177066 := proc(n) M := Matrix(n) ; for i from 1 to n do for j from 1 to n do M[i, j] := igcd(2*i-1, 2*j-1) ; end do: end do: LinearAlgebra[Determinant](M) ; end proc: # R. J. Mathar, Dec 10 2010

CROSSREFS

Cf. A001088, A037225, A059381, A059382.

Sequence in context: A192251 A104190 A152661 * A356429 A228568 A007170

Adjacent sequences: A177063 A177064 A177065 * A177067 A177068 A177069

KEYWORD

nonn

AUTHOR

John W. Layman, Dec 09 2010

STATUS

approved