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A134673 A051731 + A127448 - I where I is the Identity matrix (A023531). 3
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 (list; table; graph; refs; listen; history; text; internal format)
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..55.

FORMULA

A051731 + A127448 - A023531.

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 are:

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: A162934 A303908 A082660 * A131636 A188023 A077888

Adjacent sequences:  A134670 A134671 A134672 * A134674 A134675 A134676

KEYWORD

tabl,sign

AUTHOR

Gary W. Adamson, Nov 05 2007

STATUS

approved

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Last modified November 13 12:45 EST 2019. Contains 329094 sequences. (Running on oeis4.)