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

Author

Omar E. Pol, Feb 22 2018

Keywords

• nonn
• tabf

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.

Examples

			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;
...
		

Links

• Index entries for sequences related to sigma(n)

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.