%I #22 Jun 19 2019 17:56:50
%S 2,3,4,5,4,6,0,7,5,8,0,9,6,10,0,6,11,7,0,12,0,0,13,8,7,14,0,0,15,9,0,
%T 16,0,8,17,10,0,8,18,0,0,0,19,11,9,0,20,0,0,0,21,12,0,9,22,0,10,0,23,
%U 13,0,0,24,0,0,0,25,14,11,10,26,0,0,0,10
%N Triangle read by rows T(n,k), n>=1, k>=1, in which column k lists the positive integers interleaved with k-1 zeros, but starting from 2*k at row k^2.
%C Row sums give A060866.
%C If n is a square then the row sum gives n^(1/2) + A000203(n) otherwise the row sum gives A000203(n).
%C Row n has length A000196(n).
%C Row n has only one positive term iff n is a noncomposite number (A008578).
%C If the first element of every column is divided by 2 then we have the triangle A237273 whose row sums give A000203.
%C It appears that there are only eight rows that do not contain zeros. The indices of these rows are in A018253.
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%e Triangle begins:
%e 2;
%e 3;
%e 4;
%e 5, 4;
%e 6, 0;
%e 7, 5;
%e 8, 0;
%e 9, 6;
%e 10, 0, 6;
%e 11, 7, 0;
%e 12, 0, 0;
%e 13, 8, 7;
%e 14, 0, 0;
%e 15, 9, 0;
%e 16, 0, 8;
%e 17, 10, 0, 8;
%e 18, 0, 0, 0;
%e 19, 11, 9, 0;
%e 20, 0, 0, 0;
%e 21, 12, 0, 9;
%e 22, 0, 10, 0;
%e 23, 13, 0, 0;
%e 24, 0, 0, 0;
%e 25, 14, 11, 10;
%e 26, 0, 0, 0, 10;
%e 27, 15, 0, 0, 0;
%e 28, 0, 12, 0, 0;
%e 29, 16, 0, 11, 0;
%e 30, 0, 0, 0, 0;
%e 31, 17, 13, 0, 11;
%e ...
%Y Cf. A000196, A000203, A008578, A018253, A060866, A161901, A196020, A237270, A237273, A238442.
%K nonn,tabf
%O 1,1
%A _Omar E. Pol_, Mar 02 2014