A119948 Triangle of denominators in the square of the matrix with A[i,j] = 1/i for j <= i, 0 otherwise.

1, 4, 4, 18, 18, 9, 48, 48, 48, 16, 300, 300, 300, 100, 25, 120, 120, 120, 360, 180, 36, 980, 980, 980, 2940, 1470, 294, 49, 2240, 2240, 2240, 6720, 6720, 1344, 448, 64, 22680, 22680, 22680, 22680, 22680, 4536

Offset: 1

Author

Wolfdieter Lang, Jul 20 2006

Keywords

• nonn
• easy
• frac
• tabl

Comments

The triangle of the corresponding numerators is A119947. The rationals appear in lowest terms.

The least common multiple (LCM) of row i gives [1, 4, 18, 48, 300, 360, 2940, 6720, 22680, ...], which coincides with A081528.

Examples

			The first rows of the table are:
  [1];
  [4, 4];
  [18, 18, 9];
  [48, 48, 48, 16];
  [300, 300, 300, 100, 25];
  [120, 120, 120, 360, 180, 36]; ...
		

Crossrefs

Row sums give A119950. Row sums of the triangle of rationals always give 1.

Programs

PARI

A119948_upto(n)={my(M=matrix(n, n, i, j, (j<=i)/i)^2); vector(n, r, apply(denominator, M[r, 1..r]))} \\ M. F. Hasler, Nov 05 2019

Formula

T(i,j) = denominator((A^2)[i,j]), where the lower triangular matrix A has elements a[i,j] = 1/i if j <= i, 0 if j > i.

Extensions

Edited by M. F. Hasler, Nov 05 2019