A238288 - OEIS

%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