A143317 Triangle read by rows: A051731 * A143239.

1, 3, -1, 4, 0, -1, 7, -3, 0, 0, 6, 0, 0, 0, -1, 12, -4, -3, 0, 0, 1, 8, 0, 0, 0, 0, 0, -1, 15, -7, 0, 0, 0, 0, 0, 0, 13, 0, -4, 0, 0, 0, 0, 0, 0, 18, -6, 0, 0, -3, 0, 0, 0, 0, 1, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 28, -12, -7, 0, 0, 3, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1

Offset: 1

Author

Gary W. Adamson, Aug 07 2008

Keywords

• tabl
• sign

Comments

Left border = sigma(n), A000203.

Right border = mu(n), A008683.

Row sums = n.

It appears that T(n,k) = Sum_{d|n} mu(d)*sigma(n/d). - Joerg Arndt, Jul 31 2011

Examples

			First few rows of the triangle:
   1;
   3, -1;
   4,  0, -1;
   7, -3,  0,  0;
   6,  0,  0,  0, -1;
  12, -4, -3,  0,  0,  1;
   8,  0,  0,  0,  0,  0, -1;
  15, -7,  0,  0,  0,  0,  0,  0;
  13,  0, -4,  0,  0,  0,  0,  0,  0;
  18, -6,  0,  0, -3,  0,  0,  0,  0,  1;
  ...
		

Crossrefs

Cf. A000203, A008683, A051731, A143239.

Extensions

a(68) = -12 corrected by Georg Fischer, Jun 05 2023