A240061 - OEIS

A240061

Triangle read by rows, n>=1, 1<=k<=n. T(n,k) = number of cells in k-th row = number of cells in the k-th column of the diagram of the symmetric representation of sigma(n) in the first quadrant.

%I #25 Jun 19 2019 17:57:03

%S 1,1,2,1,1,2,1,1,2,3,1,1,1,0,3,1,1,1,3,2,4,1,1,1,1,0,0,4,1,1,1,1,3,2,

%T 1,5,1,1,1,1,1,1,2,0,5,1,1,1,1,1,3,1,2,1,6,1,1,1,1,1,1,0,0,0,0,6,1,1,

%U 1,1,1,1,4,3,4,3,1,7,1,1,1,1,1,1,1,0,0,0,0,0,7

%N Triangle read by rows, n>=1, 1<=k<=n. T(n,k) = number of cells in k-th row = number of cells in the k-th column of the diagram of the symmetric representation of sigma(n) in the first quadrant.

%C Since the diagram is symmetric the number of cells in the k-th row equals the number of cells in k-th column, see example.

%C Row sums give A000203.

%C Right border gives A008619, n >= 1.

%C If n is an odd prime then row n lists (n+1)/2 ones, ((n+1)/2 - 2) zeros, and (n+1)/2.

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

%e Triangle begins:

%e 1;

%e 1, 2;

%e 1, 1, 2;

%e 1, 1, 2, 3;

%e 1, 1, 1, 0, 3;

%e 1, 1, 1, 3, 2, 4;

%e 1, 1, 1, 1, 0, 0, 4;

%e 1, 1, 1, 1, 3, 2, 1, 5;

%e 1, 1, 1, 1, 1, 1, 2, 0, 5;

%e 1, 1, 1, 1, 1, 3, 1, 2, 1, 6;

%e 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 6;

%e 1, 1, 1, 1, 1, 1, 4, 3, 4, 3, 1, 7;

%e 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 7;

%e ...

%e For n = 9 the symmetric representation of sigma(9) = 13 in the first quadrant looks like this:

%e y

%e . Number of cells

%e ._ _ _ _ _

%e |_ _ _ _ _| 5

%e . |_ _ 0

%e . |_ | 2

%e . |_|_ _ 1

%e . | | 1

%e . . . . . . . . |_| . . x 1

%e .

%e So the 9th row of triangle is [1, 1, 1, 1, 1, 1, 2, 0, 5].

%e For n = 9 and k = 7 there are two cells in the 7th row of the diagram, also there are two cells in the 7th column of the diagram, so T(9,7) = 2.

%Y Cf. A000203, A008619, A024916, A196020, A236104, A235791, A237270, A237271, A237591, A237593, A239660, A239931-A239934, A240060.

%K nonn,tabl

%O 1,3

%A _Omar E. Pol_, Apr 26 2014