A260502 -id:A260502 - cp's OEIS frontend

A060841 Numerator of 1/det(M) where M is the n X n matrix with M[i,j] = 1/lcm(i,j).

1, 4, 18, 144, 900, 16200, 132300, 2116800, 28576800, 714420000, 8644482000, 311201352000, 4382752374000, 143169910884000, 4026653743612500, 128852919795600000, 2327405863808025000, 125679916645633350000

Offset: 1

Noam Katz (noamkj(AT)hotmail.com), May 02 2001

The value of 1/det(M) is not always an integer! For example, 1/det(35) = 5029296746186844716050163189085401314000634765625/2. - Harry J. Smith, Jul 13 2009
Conjecture: 1/det(M) is an integer only for n: 1 - 34, 36 and 38. All denominators are powers of two (A000079). But not all powers of two are present. See A260502. - Robert G. Wilson v, Aug 02 2015
Values of n at which a(n) = a(n+1): 63, 127, 255, ..., . - Robert G. Wilson v, Aug 03 2015

			a(2) = 4 because the matrix M is [1,1/2; 1/2,1/2] and det(M) = 1/4.

Robert G. Wilson v, Table of n, a(n) for n = 1..400

Cf. A000010, A001088, A060238, A260502, A260897.

d[n_] := Denominator[ Det[ Table[ GCD[1/i, 1/j], {i, n}, {j, n}]]; Array[d, 18]] (* Robert G. Wilson v, Aug 02 2015 *)

vector(20, n, numerator(1/matdet(matrix(n, n, i, j, 1/lcm(i,j))))) \\ Michel Marcus, Aug 03 2015

a(n) = (n!)^2 / (phi(1)*phi(2)*...*phi(n)) = (n!)^2 / A001088(n).

More terms from Reiner Martin, May 17 2001

A260897 Numerator of det(M) where M is the n X n matrix with M[i,j] = 1/lcm(i,j).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 8, 2, 16, 16, 32, 8, 64, 32, 64, 4, 8, 8, 256, 128, 512, 256, 2048, 256, 1024, 1024, 2048, 2048, 8192, 4096, 16384, 128, 2048, 2048, 4096, 8192, 32768, 65536, 131072, 16384, 131072

Offset: 1

Robert G. Wilson v, Aug 03 2015

nonn

All terms are powers of two (A000079).

Robert G. Wilson v, Table of n, a(n) for n = 1..500

Cf. A060841, A260502.

seq(denom(1/LinearAlgebra:-Determinant(Matrix(n,n,1/ilcm))),n=1..100); # Robert Israel, Aug 17 2015

f[n_] := Denominator[1 / Det[ Table[ 1/LCM[i, j], {i, n}, {j, n}]]]; Array[f, 73]

vector(80, n, denominator(1/matdet(matrix(n, n, i, j, 1/lcm(i, j))))) \\ Michel Marcus, Aug 04 2015

a(n) = 2^A260502(n).

cp's OEIS Frontend

A060841 Numerator of 1/det(M) where M is the n X n matrix with M[i,j] = 1/lcm(i,j).

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