A299484 Irregular triangle read by rows in which T(n,k) is the number of cells in the k-th level of the diagram of the symmetric representation of sigma(n).

1, 2, 1, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 4, 3, 2, 2, 2, 2, 2, 2, 4, 5, 2, 2, 2, 2, 4, 3, 2, 2, 2, 4, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 6, 7, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 6, 4, 2, 2, 2, 2, 2, 3, 6, 5, 2, 2, 2, 2, 2, 2, 4, 8, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 9, 6, 2, 2, 2, 2, 2

Offset

1,2

Comments

If n is an odd prime p then row n has length (p + 1)/2 and all terms in row n are 2's.

For more information about the diagram of the symmetric representation of sigma(n) see A237593 and other related sequences.

Links

Table of n, a(n) for n=1..103.

Index entries for sequences related to sigma(n)

Example

Triangle begins:
1;
2, 1;
2, 2;
2, 3, 2;
2, 2, 2;
2, 3, 4, 3;
2, 2, 2, 2;
2, 2, 4, 5, 2;
2, 2, 2, 4, 3;
2, 2, 2, 4, 6, 2;
2, 2, 2, 2, 2, 2;
2, 2, 2, 5, 6, 7, 4;
2, 2, 2, 2, 2, 2, 2;
2, 2, 2, 2, 4, 6, 4, 2;
2, 2, 2, 2, 3, 6, 5, 2;
2, 2, 2, 2, 2, 4, 8, 7, 2;
2, 2, 2, 2, 2, 2, 2, 2, 2;
2, 2, 2, 2, 2, 4, 8, 9, 6, 2;
2, 2, 2, 2, 2, 2, 2, 2, 2, 2;
...

Crossrefs

Row sums give A000203.

Row n has length A008619(n).

Column 1 is A040000.

Cf. A196020, A235791, A236104, A237048, A237270, A237271, A237591, A237593, A244050, A245092, A249351, A262611, A262626, A281010, A296508.

Sequence in context: A192394 A085033 A230254 * A327007 A336767 A096446

Adjacent sequences: A299481 A299482 A299483 * A299485 A299486 A299487

Keyword

nonn,tabf

Author

Omar E. Pol, Feb 22 2018

Status

approved