A143355 Triangle read by rows: T(n,k) = Sum_{d|n} floor(d/k).

1, 3, 1, 4, 1, 1, 7, 3, 1, 1, 6, 2, 1, 1, 1, 12, 5, 3, 1, 1, 1, 8, 3, 2, 1, 1, 1, 1, 15, 7, 3, 3, 1, 1, 1, 1, 13, 5, 4, 2, 1, 1, 1, 1, 1, 18, 8, 4, 3, 3, 1, 1, 1, 1, 1, 12, 5, 3, 2, 2, 1, 1, 1, 1, 1, 1, 28, 13, 8, 5, 3, 3, 1, 1, 1, 1, 1, 1

Offset

1,2

Links

Table of n, a(n) for n=1..78.

Formula

Equals A051731 * A010766 as infinite lower triangular matrices.

T(n,1) = sigma(n).

T(n,k) = Sum_{i=1..floor(n/k)} A135539(n,k*i). - Ridouane Oudra, Dec 17 2025

Example

First few rows of the triangle =
   1;
   3, 1;
   4, 1, 1;
   7, 3, 1, 1;
   6, 2, 1, 1, 1;
  12, 5, 3, 1, 1, 1;
   8, 3, 2, 1, 1, 1, 1;
  15, 7, 3, 3, 1, 1, 1, 1;
  ...

Crossrefs

Row sums are A143356.

Column 1 is A000203 and Column 2 is A086670.

Cf. A010766, A051731, A135539.

Sequence in context: A130314 A334466 A127057 * A143319 A078011 A010285

Adjacent sequences: A143352 A143353 A143354 * A143356 A143357 A143358

Keyword

nonn,tabl

Author

Gary W. Adamson, Aug 10 2008

Extensions

a(72) split by Georg Fischer, May 29 2023

New name from Ridouane Oudra, Dec 17 2025

Status

approved