A093412 Triangle read by rows: a(n, k) is the numerator of (n + (n-1) + ... + (n-k+1))/(1 + 2 + ... + k), 0 < k <= n.

1, 2, 1, 3, 5, 1, 4, 7, 3, 1, 5, 3, 2, 7, 1, 6, 11, 5, 9, 4, 1, 7, 13, 3, 11, 5, 9, 1, 8, 5, 7, 13, 2, 11, 5, 1, 9, 17, 4, 3, 7, 13, 3, 11, 1, 10, 19, 9, 17, 8, 15, 7, 13, 6, 1, 11, 7, 5, 19, 3, 17, 2, 5, 7, 13, 1, 12, 23, 11, 21, 10, 19, 9, 17, 8, 15, 7, 1, 13, 25, 6, 23, 11, 3, 5, 19, 9, 17, 4

Offset: 1

Author

Amarnath Murthy, Mar 30 2004

Keywords

• easy
• nonn
• tabl
• frac

Comments

A093415 gives the corresponding denominators.

Examples

			Triangle a(n,k) (with rows n >= 1 and columns k >= 1) begins as follows:
  1;
  2,  1;
  3,  5, 1;
  4,  7, 3,  1;
  5,  3, 2,  7, 1;
  6, 11, 5,  9, 4,  1;
  7, 13, 3, 11, 5,  9, 1;
  8,  5, 7, 13, 2, 11, 5,  1;
  9, 17, 4,  3, 7, 13, 3, 11, 1;
... - _Petros Hadjicostas_, Oct 20 2019
		

Crossrefs

Cf. A093413, A093414, A093415.

Formula

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

Extensions

Edited and extended by David Wasserman, Feb 01 2006