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

1,1

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.

Links

Table of n, a(n) for n=1..75.

Index entries for sequences related to sigma(n)

Example

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;
...

Crossrefs

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

Sequence in context: A309293 A244904 A338885 * A323161 A152739 A279614

Adjacent sequences: A238285 A238286 A238287 * A238289 A238290 A238291

Keyword

nonn,tabf

Author

Omar E. Pol, Mar 02 2014

Status

approved