A004199 Table of [ x/y ], where (x,y) = (1,1),(1,2),(2,1),(1,3),(2,2),(3,1),...

1, 0, 2, 0, 1, 3, 0, 0, 1, 4, 0, 0, 1, 2, 5, 0, 0, 0, 1, 2, 6, 0, 0, 0, 1, 1, 3, 7, 0, 0, 0, 0, 1, 2, 3, 8, 0, 0, 0, 0, 1, 1, 2, 4, 9, 0, 0, 0, 0, 0, 1, 1, 2, 4, 10, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 11, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 12, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 3, 6, 13, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 6, 14

Offset: 1

Author

David W. Wilson

Keywords

• tabl
• nonn

Comments

Entry in row n and column k is also the number of multiples of k less than or equal to n, n,k >= 1. - L. Edson Jeffery, Aug 31 2014

Examples

			Array begins:
  1, 0, 0, 0, 0, 0, 0, 0, ...
  2, 1, 0, 0, 0, 0, 0, 0, ...
  3, 1, 1, 0, 0, 0, 0, 0, ...
  4, 2, 1, 1, 0, 0, 0, 0, ...
  5, 2, 1, 1, 1, 0, 0, 0, ...
  ...
		

Crossrefs

Cf. A002541 (antidiagonal sums).

Cf. A010766 (same sequence as triangle, omitting the zeros), A010783.

Programs

Mathematica

(* Array version: *)
Grid[Table[Floor[n/k], {n, 14}, {k, 14}]] (* L. Edson Jeffery, Aug 31 2014 *)
(* Array antidiagonals flattened: *)
Flatten[Table[Floor[(n - k + 1)/k], {n, 14}, {k, n}]] (* L. Edson Jeffery, Aug 31 2014 *)

Formula

Sum_{k=1..n} a(n-k+1,k) = A002541(n+1).