A127505 Triangle T(n,k) = mobius(n/k)*phi(k) if k|n, otherwise T(n,k)=0; 1<=k<=n.

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

Offset: 1

Author

Gary W. Adamson, Jan 17 2007

Keywords

• easy
• tabl
• sign

Examples

			First few rows of the triangle are:
1;
-1, 1;
-1, 0, 2;
0, -1, 0, 2;
-1, 0, 0, 0, 4;
1, -1, -2, 0, 0, 2;
...
		

Crossrefs

Cf. A051731, A000010 (diagonal n=k), A007431 (row sums), A008683 (column k=1).

Formula

T(n,k) = sum_{j=k..n} A054525(n,j)*A130207(j,k), 1<=k<=n.