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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
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.
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.
Sequence in context: A192394 A085033 A230254 * A327007 A336767 A096446
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Feb 22 2018
STATUS
approved