A093415 Triangle read by rows: a(n, k) is the denominator of (n + (n-1) + ... + (n-k+1))/(1 + 2 + ... + k), 0 < k <= n.

1, 1, 1, 1, 3, 1, 1, 3, 2, 1, 1, 1, 1, 5, 1, 1, 3, 2, 5, 3, 1, 1, 3, 1, 5, 3, 7, 1, 1, 1, 2, 5, 1, 7, 4, 1, 1, 3, 1, 1, 3, 7, 2, 9, 1, 1, 3, 2, 5, 3, 7, 4, 9, 5, 1, 1, 1, 1, 5, 1, 7, 1, 3, 5, 11, 1, 1, 3, 2, 5, 3, 7, 4, 9, 5, 11, 6, 1, 1, 3, 1, 5, 3, 1, 2, 9, 5, 11, 3, 13, 1, 1, 1, 2, 1, 1, 7, 4, 3, 1, 11, 2

Offset: 1

Author

Amarnath Murthy, Mar 30 2004

Keywords

• easy
• nonn
• tabl
• frac

Comments

A093412 gives the corresponding numerators.

A109613(n+1) - 2 = 2*floor((n+1)/2) - 1 is the largest number in row n. [Corrected by Petros Hadjicostas, Oct 20 2019]

Examples

			Triangle a(n,k) (with rows n >= 1 and columns k >= 1) begins as follows:
  1;
  1, 1;
  1, 3, 1;
  1, 3, 2, 1;
  1, 1, 1, 5, 1;
  1, 3, 2, 5, 3, 1;
  1, 3, 1, 5, 3, 7, 1;
  1, 1, 2, 5, 1, 7, 4, 1;
  1, 3, 1, 1, 3, 7, 2, 9, 1;
... - _Petros Hadjicostas_, Oct 20 2019
		

Crossrefs

Cf. A109613, A093412, A093413, A093414, A093417.

Formula

a(n, k) = (k+1)/gcd(2n+2, k+1).

Extensions

Edited and extended by David Wasserman, Feb 01 2006