A143724 Triangle read by rows, inverse Möbius transform of a diagonalized matrix of A116477.

1, 1, 2, 1, 0, 4, 1, 2, 0, 5, 1, 0, 0, 0, 9, 1, 2, 4, 0, 0, 7, 1, 0, 0, 0, 0, 0, 15, 1, 2, 0, 5, 0, 0, 0, 12, 1, 0, 4, 0, 0, 0, 0, 0, 18, 1, 2, 0, 0, 9, 0, 0, 0, 0, 15, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 1, 2, 4, 5, 0, 7, 0, 0, 0, 0, 0, 16

Offset: 1

Author

Gary W. Adamson, Aug 29 2008

Keywords

• nonn
• tabl

Comments

For n-th row of the triangle, the inverse Möbius transform extracts A116477(k) such that k divides n; 0 otherwise.

Row sums = A006218: (1, 3, 5, 8, 10, 14, 16, ...).

Examples

			First few rows of the triangle:
1;
1, 2;
1, 0, 4;
1, 2, 0, 5;
1, 0, 0, 0, 9;
1, 2, 4, 0, 0, 7;
1, 0, 0, 0, 0, 0, 15;
1, 2, 0, 5, 0, 0,  0, 12;
...
Example: The divisors of 8 are (1, 2, 4, 8) so row 8 = (1, 2, 0, 5, 0, 0, 0, 12).
		

Crossrefs

Cf. A006218, A051731, A116477.

Formula

Triangle read by rows, A051731 * (A116477 * 0^(n-k)); 1 <= k <= n.

Extensions

Diagonal sequence corrected to A116477 by Georg Fischer, Jun 27 2023