A229944 Triangle read by rows in which T(2n-2,k) = n/k if k divides n and n/k > sqrt(n), otherwise 0, for n >= 2. Also T(2n-1,k) = k if k divides n, otherwise 0, for n >= 1. Row lengths are the same row lengths of A229940.

1, 2, 1, 3, 1, 4, 1, 2, 5, 0, 1, 0, 6, 3, 1, 2, 7, 0, 1, 0, 8, 4, 1, 2, 9, 0, 1, 0, 3, 10, 5, 0, 1, 2, 0, 11, 0, 0, 1, 0, 0, 12, 6, 4, 1, 2, 3, 13, 0, 0, 1, 0, 0, 14, 7, 0, 1, 2, 0, 15, 0, 5, 1, 0, 3, 16, 8, 0, 1, 2, 0, 4, 17, 0, 0, 0, 1, 0, 0, 0, 18, 9, 6, 0, 1, 2, 3, 0

Offset: 1

Author

Omar E. Pol, Oct 05 2013

Keywords

• nonn
• tabf

Comments

The positive terms are also the divisors associated with the exposed endpoints of the toothpick structure of A229950 which is related to A000005. Note that the exposed toothpick endpoints are equivalent to the vertices of the graph mentioned in A229940. See link section.

Examples

			Triangle begins:
1;
2;
1;
3;
1;
4;
1,  2;
5,  0;
1,  0;
6,  3;
1,  2;
7,  0;
1,  0;
8,  4;
1,  2;
9,  0;
1,  0,  3;
10, 5,  0;
1,  2,  0;
11, 0,  0;
1,  0,  0;
12, 6,  4;
1,  2,  3;
13, 0,  0;
1,  0,  0;
14, 7,  0;
1,  2,  0;
15, 0,  5;
1,  0,  3;
16, 8,  0;
1,  2,  0,  4;
...
		

Links

• Omar E. Pol, Illustration of initial terms of the divisor function (A000005), see the third picture.

Crossrefs

Cf. A000005, A000203, A229940, A229942, A229950, A229951.