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

1,2

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.

Links

Table of n, a(n) for n=1..88.

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

Example

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;
...

Crossrefs

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

Sequence in context: A255810 A210256 A332422 * A366421 A218533 A328578

Adjacent sequences: A229941 A229942 A229943 * A229945 A229946 A229947

Keyword

nonn,tabf

Author

Omar E. Pol, Oct 05 2013

Status

approved