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

1,3

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.

Links

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

Formula

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

Example

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;
  ...

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 *)

Prog

(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 */
(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

Crossrefs

Cf. A051731, A127093.

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

Cf. A000142 (determinant).

Cf. A134866.

Sequence in context: A284373 A104610 A138684 * A364082 A074927 A139605

Adjacent sequences: A132439 A132440 A132441 * A132443 A132444 A132445

Keyword

nonn,tabl

Author

Gary W. Adamson, Nov 14 2007

Extensions

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

Name edited by Michel Marcus, Dec 21 2022

Status

approved