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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 A240061 #25 Jun 19 2019 17:57:03
%S A240061 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 A240061 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 A240061 1,1,1,1,4,3,4,3,1,7,1,1,1,1,1,1,1,0,0,0,0,0,7
%N 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.
%C A240061 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 A240061 Row sums give A000203.
%C A240061 Right border gives A008619, n >= 1.
%C A240061 If n is an odd prime then row n lists (n+1)/2 ones, ((n+1)/2 - 2) zeros, and (n+1)/2.
%H A240061 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%e A240061 Triangle begins:
%e A240061 1;
%e A240061 1, 2;
%e A240061 1, 1, 2;
%e A240061 1, 1, 2, 3;
%e A240061 1, 1, 1, 0, 3;
%e A240061 1, 1, 1, 3, 2, 4;
%e A240061 1, 1, 1, 1, 0, 0, 4;
%e A240061 1, 1, 1, 1, 3, 2, 1, 5;
%e A240061 1, 1, 1, 1, 1, 1, 2, 0, 5;
%e A240061 1, 1, 1, 1, 1, 3, 1, 2, 1, 6;
%e A240061 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 6;
%e A240061 1, 1, 1, 1, 1, 1, 4, 3, 4, 3, 1, 7;
%e A240061 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 7;
%e A240061 ...
%e A240061 For n = 9 the symmetric representation of sigma(9) = 13 in the first quadrant looks like this:
%e A240061 y
%e A240061 .                               Number of cells
%e A240061 ._ _ _ _ _
%e A240061 |_ _ _ _ _|                            5
%e A240061 .         |_ _                         0
%e A240061 .         |_  |                        2
%e A240061 .           |_|_ _                     1
%e A240061 .               | |                    1
%e A240061 .               | |                    1
%e A240061 .               | |                    1
%e A240061 .               | |                    1
%e A240061 . . . . . . . . |_| . . x              1
%e A240061 .
%e A240061 So the 9th row of triangle is [1, 1, 1, 1, 1, 1, 2, 0, 5].
%e A240061 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 A240061 Cf. A000203, A008619, A024916, A196020, A236104, A235791, A237270, A237271, A237591, A237593, A239660, A239931-A239934, A240060.
%K A240061 nonn,tabl
%O A240061 1,3
%A A240061 _Omar E. Pol_, Apr 26 2014