A238288 Triangle read by rows T(n,k), n>=1, k>=1, in which column k lists the positive integers interleaved with k-1 zeros, but starting from 2*k at row k^2.

2, 3, 4, 5, 4, 6, 0, 7, 5, 8, 0, 9, 6, 10, 0, 6, 11, 7, 0, 12, 0, 0, 13, 8, 7, 14, 0, 0, 15, 9, 0, 16, 0, 8, 17, 10, 0, 8, 18, 0, 0, 0, 19, 11, 9, 0, 20, 0, 0, 0, 21, 12, 0, 9, 22, 0, 10, 0, 23, 13, 0, 0, 24, 0, 0, 0, 25, 14, 11, 10, 26, 0, 0, 0, 10

Offset: 1

Author

Omar E. Pol, Mar 02 2014

Keywords

• nonn
• tabf

Comments

Row sums give A060866.

If n is a square then the row sum gives n^(1/2) + A000203(n) otherwise the row sum gives A000203(n).

Row n has length A000196(n).

Row n has only one positive term iff n is a noncomposite number (A008578).

If the first element of every column is divided by 2 then we have the triangle A237273 whose row sums give A000203.

It appears that there are only eight rows that do not contain zeros. The indices of these rows are in A018253.

Examples

			Triangle begins:
2;
3;
4;
5,   4;
6,   0;
7,   5;
8,   0;
9,   6;
10,  0,  6;
11,  7,  0;
12,  0,  0;
13,  8,  7;
14,  0,  0;
15,  9,  0;
16,  0,  8;
17, 10,  0,  8;
18,  0,  0,  0;
19, 11,  9,  0;
20,  0,  0,  0;
21, 12,  0,  9;
22,  0, 10,  0;
23, 13,  0,  0;
24,  0,  0,  0;
25, 14, 11, 10;
26,  0,  0,  0,  10;
27, 15,  0,  0,   0;
28,  0, 12,  0,   0;
29, 16,  0, 11,   0;
30,  0,  0,  0,   0;
31, 17, 13,  0,  11;
...
		

Links

• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000196, A000203, A008578, A018253, A060866, A161901, A196020, A237270, A237273, A238442.