A127475 Triangle T(n,k) read by rows: T(n,k) = mu(n)*phi(k) if k|n, else T(n,k)=0.

1, -1, -1, -1, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, -4, 1, 1, 2, 0, 0, 2, -1, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 4, 0, 0, 0, 0, 4, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12

Offset: 1

Author

Gary W. Adamson, Jan 15 2007

Keywords

• tabl
• easy
• sign

Examples

			The triangle starts in row n=1 as:
1;
-1, -1;
-1, 0, -2;
0, 0, 0, 0;
-1, 0, 0, 0, -4;
1, 1, 2, 0, 0, 2;
-1, 0, 0, 0, 0, 0, -6;
...
		

Crossrefs

Cf. A008683, A054522, A055615 (row sums), A097945, A023900.

Formula

T(n,k) = A054522(n,k)*A008683(n).

T(n,1) = A008683(n) = mu(n).

T(n,n) = A097945(n).