cp's OEIS Frontend

A238288 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.

%I A238288 #22 Jun 19 2019 17:56:50
%S A238288 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 A238288 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 A238288 13,0,0,24,0,0,0,25,14,11,10,26,0,0,0,10
%N A238288 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 A238288 Row sums give A060866.
%C A238288 If n is a square then the row sum gives n^(1/2) + A000203(n) otherwise the row sum gives A000203(n).
%C A238288 Row n has length A000196(n).
%C A238288 Row n has only one positive term iff n is a noncomposite number (A008578).
%C A238288 If the first element of every column is divided by 2 then we have the triangle A237273 whose row sums give A000203.
%C A238288 It appears that there are only eight rows that do not contain zeros. The indices of these rows are in A018253.
%H A238288 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%e A238288 Triangle begins:
%e A238288 2;
%e A238288 3;
%e A238288 4;
%e A238288 5,   4;
%e A238288 6,   0;
%e A238288 7,   5;
%e A238288 8,   0;
%e A238288 9,   6;
%e A238288 10,  0,  6;
%e A238288 11,  7,  0;
%e A238288 12,  0,  0;
%e A238288 13,  8,  7;
%e A238288 14,  0,  0;
%e A238288 15,  9,  0;
%e A238288 16,  0,  8;
%e A238288 17, 10,  0,  8;
%e A238288 18,  0,  0,  0;
%e A238288 19, 11,  9,  0;
%e A238288 20,  0,  0,  0;
%e A238288 21, 12,  0,  9;
%e A238288 22,  0, 10,  0;
%e A238288 23, 13,  0,  0;
%e A238288 24,  0,  0,  0;
%e A238288 25, 14, 11, 10;
%e A238288 26,  0,  0,  0,  10;
%e A238288 27, 15,  0,  0,   0;
%e A238288 28,  0, 12,  0,   0;
%e A238288 29, 16,  0, 11,   0;
%e A238288 30,  0,  0,  0,   0;
%e A238288 31, 17, 13,  0,  11;
%e A238288 ...
%Y A238288 Cf. A000196, A000203, A008578, A018253, A060866, A161901, A196020, A237270, A237273, A238442.
%K A238288 nonn,tabf
%O A238288 1,1
%A A238288 _Omar E. Pol_, Mar 02 2014