A132442 Triangle whose n-th row consists of the first n terms of the n-th row of A134866.

1, 1, 3, 1, 1, 4, 1, 3, 1, 7, 1, 1, 1, 1, 6, 1, 3, 4, 3, 1, 12, 1, 1, 1, 1, 1, 1, 8, 1, 3, 1, 7, 1, 3, 1, 15, 1, 1, 4, 1, 1, 4, 1, 1, 13, 1, 3, 1, 3, 6, 3, 1, 3, 1, 18, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 1, 3, 4, 7, 1, 12, 1, 7, 4, 3, 1, 28, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 14, 1, 3, 1, 3, 1, 3, 8, 3, 1, 3, 1, 3, 1, 24

Offset: 1

Author

Gary W. Adamson, Nov 14 2007

Keywords

• nonn
• tabl

Comments

Previous name: Triangle, n-th row = first n terms of n-th row of an array formed by A051731 * A127093 (transform).

Right border = sigma(n), A000203.

Row sums = A038040.

The function T(n,k) = T(k,n) is defined for k > n, but only the values of k in 1..n as a triangular array are listed here.

Examples

			First few rows of the A134866 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, ...
  1,  3,  4,  3,  1, 12,  1, ...
  ...
First few rows of the triangle:
  1;
  1,  3;
  1,  1,  4;
  1,  3,  1,  7;
  1,  1,  1,  1,  6;
  1,  3,  4,  3,  1, 12;
  1,  1,  1,  1,  1,  1,  8;
  1,  3,  1,  7,  1,  3,  1, 15;
  ...
		

Links

• Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Crossrefs

Cf. A051731, A127093.

Cf. A038040 (row sums), A000203 (right border), A050873 (gcd(n,k)).

Cf. A000142 (determinant).

Cf. A134866.

Programs

Haskell

a132442 n k = a132442_tabl !! (n-1) !! (k-1)
a132442_row n = a132442_tabl !! (n-1)
a132442_tabl = map (map a000203) a050873_tabl
-- Reinhard Zumkeller, Dec 12 2015

Mathematica

T[ n_, k_] := If[ n < 1 || k < 1, 0, If[ k > n, T[ k, n], If[ k == 1, 1, If[ n > k, T[ k, Mod[ n, k, 1]],  DivisorSigma [1, n]]]]] (* Michael Somos, Jul 18 2011 *)

PARI

{T(n, k) = if( n<1 || k<1, 0, if( k>n, T(k, n), if( k==1, 1, if( n>k, T(k, (n-1)%k+1), sigma( n)))))} /* Michael Somos, Jul 18 2011 */

Formula

T(n,k) = A000203(gcd(n,k)). - Reinhard Zumkeller, Dec 12 2015

Extensions

Missing T(10,9) = 1 inserted by Reinhard Zumkeller, Dec 12 2015

Name edited by Michel Marcus, Dec 21 2022