A060841 -id:A060841 - cp's OEIS frontend

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

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).

A260502 Log_2 of the 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

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 3, 1, 4, 4, 5, 3, 6, 5, 6, 2, 3, 3, 8, 7, 9, 8, 11, 8, 10, 10, 11, 11, 13, 12, 14, 7, 11, 11, 12, 13, 15, 16, 17, 14, 17, 17, 20, 18, 20, 21, 22, 19, 20, 21, 22, 21, 27, 26, 29, 26, 29

Offset: 1

Robert G. Wilson v, Aug 02 2015

nonn

Powers of two not present in A260897: 23, 24, 25, 28, 38, 46, 47, 49, 55, 63, 64, 69, ..., .

			a(4) = 0 because for n=4 det(M) = 1/144.
a(35) = 1 because for n=35 det(M) equals 2/5029296746186844716050163189085401314000634765625.

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

Cf. A060841, A007814, A260897.

f[n_] := Log2@ Numerator@ Det@ Table[ 1/LCM[i, j], {i, n}, {j, n}]; Array[f, 85]

vector(80, n, valuation(denominator(1/matdet(matrix(n, n, i, j, 1/lcm(i, j)))), 2)) \\ Michel Marcus, Aug 04 2015

a(n) = A007814(A260897(n)).

A260908 Numerator of 1/det(M) where M is the n X n matrix with M[i,j] = 1/gcd(i,j).

Original entry on oeis.org

1, -2, 3, -12, 15, 45, -105, 420, -1890, -4725, 10395, 31185, -135135, -315315, -4729725, 4729725, -80405325, -723647925, 1527701175, 7638505875, 53469541125, 117632990475, -245959889175, -737879667525, 18446991688125, 79936963981875, -2158298027510625

Offset: 1

Robert G. Wilson v, Aug 04 2015

sign

Negative terms for n: 2, 4, 7, 9, 10, 13, 14, 15, 17, 18, 23, 24, 27, 28, 30, ..., .

Cf. A060841, A260909.

f[n_] := 1/Det[ Table[ 1/GCD[i, j], {i, n}, {j, n}]]; Numerator@ Array[f, 27]

vector(40, n, numerator(1/matdet(matrix(n, n, i, j, 1/gcd(i, j))))) \\ Michel Marcus, Aug 06 2015

cp's OEIS Frontend

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

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A260502 Log_2 of the numerator of det(M) where M is the n X n matrix with M[i,j] = 1/lcm(i,j).

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A260908 Numerator of 1/det(M) where M is the n X n matrix with M[i,j] = 1/gcd(i,j).

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Mathematica

PARI