A134673 A051731 + A127448 - I where I is the Identity matrix (A023531).

1, 0, 2, 0, 0, 3, 1, -1, 0, 4, 0, 0, 0, 0, 5, 2, -1, -2, 0, 0, 6, 0, 0, 0, 0, 0, 0, 7, 1, 1, 0, -3, 0, 0, 0, 8, 1, 0, -2, 0, 0, 0, 0, 0, 9, 2, -1, 0, 0, -4, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 1, 3, 1, -3, 0, -5, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 2, -1

Offset

1,3

Comments

Row sums = A073757: (1, 2, 3, 4, 5, 5, 7, 7, 8, 7, ...).

Links

Table of n, a(n) for n=1..93.

Formula

a(n) = A051731(n) + A127448(n) - A023531(n).

T(n,k) = k*A008683(n/k) + 1 if k divides n and k < n, T(n,k)=n for k=n, and T(n,k)=0 otherwise. - Max Alekseyev, Jan 07 2015

Example

First few rows of the triangle:
  1;
  0,  2;
  0,  0,  3;
  1, -1,  0,  4;
  0,  0,  0,  0,  5;
  2, -1, -2,  0,  0,  6;
  0,  0,  0,  0,  0,  0,  7;
  1,  1,  0, -3,  0,  0,  0,  8;
  ... [Typo corrected by N. J. A. Sloane, May 22 2010]

Prog

(PARI) A134673(n, k) = if(n%k, 0, if(k==n, n, k*moebius(n/k)+1)); /* Max Alekseyev, Jan 07 2015 */

Crossrefs

Cf. A127448, A073757, A051731.

Sequence in context: A303908 A351592 A082660 * A131636 A188023 A077888

Adjacent sequences: A134670 A134671 A134672 * A134674 A134675 A134676

Keyword

tabl,sign

Author

Gary W. Adamson, Nov 05 2007

Extensions

More terms from Max Alekseyev, Apr 03 2022

Status

approved