A141846 Triangle read by rows: A051731 * A051953^(n-k) * 0^(n-k), 1 <= k <= n.

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

Offset: 1

Author

Gary W. Adamson, Jul 11 2008

Keywords

• nonn
• tabl

Comments

Row sums = A001065: (0, 1, 1, 3, 1, 6, 1, 7, 4, 8,...).

n-th row = (p-1) zeros followed by 1, iff n is prime.

For T(n,k), k divides n if k not = 0.

Examples

			First few rows of the triangle =
0;
0, 1;
0, 0, 1;
0, 1, 0, 2;
0, 0, 0, 0, 1;
0, 1, 1, 0, 0, 4;
0, 0, 0, 0, 0, 0, 1;
0, 1, 0, 2, 0, 0, 0, 4;
0, 0, 1, 0, 0, 0, 0, 0, 3;
0, 1, 0, 0, 1, 0, 0, 0, 0, 6;
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
0, 1, 1, 2, 0, 4, 0, 0, 0, 0, 0, 8;
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 8;
...
		

Crossrefs

Cf. A051953, A001065.

Formula

Triangle read by rows, A051731 * A051953^(n-k); where A051953^(n-k) = an infinite lower triangular matrix with A051953 (0, 1, 1, 2, 1, 4, 1, 4, 3, 6, 1, 8,...) in the main diagonal and the rest zeros. A051731 = inverse Mobius transform.