A134867 A010766 * A000012.

1, 3, 1, 5, 2, 1, 8, 4, 2, 1, 10, 5, 3, 2, 1, 14, 8, 5, 3, 2, 1, 16, 9, 6, 4, 3, 2, 1, 20, 12, 8, 6, 4, 3, 2, 1, 23, 14, 10, 7, 5, 4, 3, 2, 1, 27, 17, 12, 9, 7, 5, 4, 3, 2, 1, 29, 18, 13, 10, 8, 6, 5, 4, 3, 2, 1, 35, 23, 17, 13, 10, 8, 6, 5, 4, 3, 2, 1, 37, 24, 18, 14, 11, 9, 7, 6, 5, 4, 3, 2, 1

Offset: 1

Author

Gary W. Adamson, Nov 14 2007

Keywords

• nonn
• tabl

Examples

			First few rows of the triangle:
   1;
   3,  1;
   5,  2,  1;
   8,  4,  2, 1;
  10,  5,  3, 2, 1;
  14,  8,  5, 3, 2, 1;
  16,  9,  6, 4, 3, 2, 1;
  20, 12,  8, 6, 4, 3, 2, 1;
  23, 14, 10, 7, 5, 4, 3, 2, 1;
  27, 17, 12, 9, 7, 5, 4, 3, 2, 1;
  ...
		

Crossrefs

Column k=1..4 give: A006218, A002541, A366968, A366972.

Row sums give A024916.

Cf. A010766, A135539.

Programs

Mathematica

t = Table[Sum[Floor[n/h], {h, k, n}], {n, 0, 10}, {k, 1, n}];
u = Flatten[t]  (* A134867 array *)
TableForm[t]    (* A134867 sequence *)
(* Clark Kimberling, Oct 11 2014 *)

PARI

T(n, k) = sum(j=k, n, n\j); \\ Seiichi Manyama, Oct 30 2023

Formula

A010766 * A000012 as infinite lower triangular matrices.

Triangle read by rows, partial row sums of A010766 starting fromt the right.

G.f. of column k: 1/(1-x) * Sum_{j>=1} x^(k*j)/(1-x^j) = 1/(1-x) * Sum_{j>=k} x^j/(1-x^j). - Seiichi Manyama, Oct 30 2023

Extensions

More terms from Seiichi Manyama, Oct 30 2023