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).

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

Author

Robert G. Wilson v, Aug 02 2015

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A060841, A007814, A260897.

Programs

Mathematica

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

PARI

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

Formula

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