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

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

Author

Robert G. Wilson v, Aug 04 2015

Keywords

• sign

Comments

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

Crossrefs

Cf. A060841, A260909.

Programs

Mathematica

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

PARI

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