A299484 - OEIS

%I #29 Jun 19 2019 17:56:17

%S 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,

%T 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,

%U 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

%N 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).

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

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

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%e Triangle begins:

%e 1;

%e 2, 1;

%e 2, 2;

%e 2, 3, 2;

%e 2, 2, 2;

%e 2, 3, 4, 3;

%e 2, 2, 2, 2;

%e 2, 2, 4, 5, 2;

%e 2, 2, 2, 4, 3;

%e 2, 2, 2, 4, 6, 2;

%e 2, 2, 2, 2, 2, 2;

%e 2, 2, 2, 5, 6, 7, 4;

%e 2, 2, 2, 2, 2, 2, 2;

%e 2, 2, 2, 2, 4, 6, 4, 2;

%e 2, 2, 2, 2, 3, 6, 5, 2;

%e 2, 2, 2, 2, 2, 4, 8, 7, 2;

%e 2, 2, 2, 2, 2, 2, 2, 2, 2;

%e 2, 2, 2, 2, 2, 4, 8, 9, 6, 2;

%e 2, 2, 2, 2, 2, 2, 2, 2, 2, 2;

%e ...

%Y Row sums give A000203.

%Y Row n has length A008619(n).

%Y Column 1 is A040000.

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

%K nonn,tabf

%O 1,2

%A _Omar E. Pol_, Feb 22 2018