A127476 Triangle T(n,k) = sum_{j=k..n, gcd(n,j)=1, k|j} phi(k).

1, 1, 0, 2, 1, 0, 2, 0, 2, 0, 4, 2, 2, 2, 0, 2, 0, 0, 0, 4, 0, 6, 3, 4, 2, 4, 2, 0, 4, 0, 2, 0, 4, 0, 6, 0, 6, 3, 0, 4, 4, 0, 6, 4, 0, 4, 0, 4, 0, 0, 0, 6, 0, 6, 0, 10, 5, 6, 4, 8, 2, 6, 4, 6, 4, 0, 4, 0, 0, 0, 4, 0, 6, 0, 0, 0, 10, 0

Offset: 1

Author

Gary W. Adamson, Jan 15 2007

Keywords

• nonn
• tabl

Examples

			First few rows of the triangle are:
1;
1, 0;
2, 1, 0;
2, 0, 2, 0;
4, 2, 2, 2, 0;
2, 0, 0, 0, 4, 0;
6, 3, 4, 2, 4, 2, 0;
4, 0, 2, 0, 4, 0, 6, 0;
...
		

Crossrefs

Cf. A054521, A054522, A023896 (row sums), A000010.

Formula

T(n,k) = sum_{j=k..n} A054521(n,j) * A054522(j,k), product of the two infinite lower triangular matrices.

T(n,1) = A000010(n).