A134866 Table read by antidiagonals: T(n,k) = sigma(gcd(n,k)).

1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 3, 4, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 7, 1, 3, 1, 1, 1, 4, 1, 1, 4, 1, 1, 1, 3, 1, 3, 6, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 4, 7, 1, 12, 1, 7, 4, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 3, 8, 3, 1, 3, 1, 3, 1

Offset: 1

Author

Gary W. Adamson, Nov 14 2007

Keywords

• nonn
• tabl

Comments

Previous name was: Triangle, antidiagonals of an array formed by A051731 * A127093 (transform).

Row sums give A094471.

Examples

			First few rows of the array:
  1, 1, 1, 1, 1, 1, 1, ...
  1, 3, 1, 3, 1, 3, 1, ...
  1, 1, 4, 1, 1, 4, 1, ...
  1, 3, 1, 7, 1, 3, 1, ...
  1, 1, 1, 1, 6, 1, 1, ...
  ...
First antidiagonals:
  1;
  1, 1;
  1, 3, 1;
  1, 1, 1, 1;
  1, 3, 4, 3, 1;
  1, 1, 1, 1, 1, 1;
  1, 3, 1, 7, 1, 3, 1;
  1, 1, 4, 1, 1, 4, 1, 1;
  1, 3, 1, 3, 6, 3, 1, 3, 1;
  ...
		

Links

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

Crossrefs

Cf. A051731, A127093, A094471, A132442.

Programs

Mathematica

Table[DivisorSigma[1, GCD[#, k]] &[n - k + 1], {n, 13}, {k, n}] // Flatten (* Michael De Vlieger, Dec 19 2022 *)

PARI

T(n, k) = sigma(gcd(n, k)); \\ Michel Marcus, Dec 19 2022

Formula

T(n,k) = A000203(A050873(n,k)). - Michel Marcus, Dec 19 2022

Extensions

New name and data corrected by Michel Marcus, Dec 19 2022