A187954 Triangle by rows, divisors of odd integers.

1, 1, 3, 1, 0, 5, 1, 0, 0, 7, 1, 3, 0, 0, 9, 1, 0, 0, 0, 0, 11, 1, 0, 0, 0, 0, 0, 13, 1, 3, 5, 0, 0, 0, 0, 15, 1, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 19, 1, 3, 0, 7, 0, 0, 0, 0, 0, 0, 21

Offset: 0

Author

Gary W. Adamson, Mar 16 2011

Keywords

• nonn
• tabl

Comments

Row sums = A008438: (1, 4, 6, 8, 13, 12, 14,...)

Examples

			First few rows of the triangle =
1
1, 3
1, 0, 5
1, 0, 0, 7
1, 3, 0, 0, 9
1, 0, 0, 0, 0, 11
1, 0, 0, 0, 0, 0, 13
1, 3, 5, 0, 0, 0, 0, 15
1, 0, 0, 0, 0, 0, 0, 0, 17
1, 0, 0, 0, 0, 0, 0, 0, 0, 19
1, 3, 0, 7, 0, 0, 0, 0, 0, 0, 21
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23
1, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25
1, 3, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 27
...
Example: Row 4 = (1, 3, 0, 0, 9) since the divisors of 9 are (1, 3, and 9).
		

Crossrefs

Cf. A114000, A008438

Formula

Let A = A114000 and B = a diagonalized variant of the odd integers ((1, 3, 5, 7, 9,...) as the right diagonal and the rest zeros). The triangle = A*B as infinite lower triangular matrices.