A075993 Triangle read by rows: T(n,m) is the number of integers k such that floor(n/k) = m, n >= 1, k = 1..n.

1, 1, 1, 2, 0, 1, 2, 1, 0, 1, 3, 1, 0, 0, 1, 3, 1, 1, 0, 0, 1, 4, 1, 1, 0, 0, 0, 1, 4, 2, 0, 1, 0, 0, 0, 1, 5, 1, 1, 1, 0, 0, 0, 0, 1, 5, 2, 1, 0, 1, 0, 0, 0, 0, 1, 6, 2, 1, 0, 1, 0, 0, 0, 0, 0, 1, 6, 2, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 7, 2, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 7, 3, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1

Offset

1,4

Comments

The sum of numbers in row n is n.

Number of terms > 0 per row: Sum_{k=1..n} A063524(T(n,k)) = A055086(n). - Reinhard Zumkeller, Apr 06 2006

Links

Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows 1 <= n <= 150, flattened)

Formula

T(n, m) = floor(n/m) - floor(n/(m+1)).

Example

T(5, 1) = 3 counts k such that floor(5/k) = 1, namely k = 5, 4, 3.
First 10 rows:
  1
  1 1
  2 0 1
  2 1 0 1
  3 1 0 0 1
  3 1 1 0 0 1
  4 1 1 0 0 0 1
  4 2 0 1 0 0 0 1
  5 1 1 1 0 0 0 0 1
  5 2 1 0 1 0 0 0 0 1

Mathematica

Table[Floor[n/m] - Floor[n/(m + 1)], {n, 14}, {m, n}] // Flatten (* Michael De Vlieger, Jan 14 2022 *)

Crossrefs

Columns 1, 2, 3 are essentially A004526, A008615, A008679.

Cf. A010766.

Sequence in context: A168121 A158948 A140224 * A117170 A117466 A136266

Adjacent sequences: A075990 A075991 A075992 * A075994 A075995 A075996

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 28 2002

Status

approved