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

0,3

Comments

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

Links

Table of n, a(n) for n=0..64.

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.

Example

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

Sequence in context: A127627 A154792 A185911 * A119302 A134560 A127626

Adjacent sequences: A187951 A187952 A187953 * A187955 A187956 A187957

Keyword

nonn,tabl

Author

Gary W. Adamson, Mar 16 2011

Status

approved