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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, 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, ...).
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
KEYWORD
tabl,sign
AUTHOR
Gary W. Adamson, Nov 05 2007
EXTENSIONS
More terms from Max Alekseyev, Apr 03 2022
STATUS
approved