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A299693 Irregular triangle read by rows in which row n lists the total sum of the divisors of all numbers k such that the largest Dyck path of the symmetric representation of sigma(k) contains the point (n,n); or row n is 0 if no such k exists.

%I A299693 #25 Nov 24 2024 20:40:37
%S A299693 1,3,4,7,6,0,12,8,15,13,18,12,0,28,14,24,0,24,31,18,39,20,0,42,32,36,
%T A299693 24,0,60,31,42,40,0,56,30,0,72,32,63,48,54,0,48,91,38,60,56,0,90,42,0,
%U A299693 96,44,84,0,78,72,48,0,124,57,93,72,98,54,0,120,72,0,120,80,90,60,0,168,62,96,0,104,127,84,0
%N A299693 Irregular triangle read by rows in which row n lists the total sum of the divisors of all numbers k such that the largest Dyck path of the symmetric representation of sigma(k) contains the point (n,n); or row n is 0 if no such k exists.
%F A299693 T(n,m) = A000203(A279385(n,m)) if A279385(n,m) > 0, otherwise T(n,m) = 0.
%e A299693 Triangle begins:
%e A299693    1;
%e A299693    3,  4;
%e A299693    7,  6;
%e A299693    0;
%e A299693   12,  8;
%e A299693   15;
%e A299693   13, 18, 12;
%e A299693    0;
%e A299693   28, 14, 24;
%e A299693    0;
%e A299693   24;
%e A299693   31, 18;
%e A299693   39, 20;
%e A299693    0;
%e A299693   42, 32, 36, 24;
%e A299693    0;
%e A299693 ...
%Y A299693 Nonzero terms give A000203.
%Y A299693 Row sums give A299472.
%Y A299693 Cf. A259179(n) is the number of positive terms in row n.
%Y A299693 Cf. A071562, A196020, A235791, A236104, A237048, A237591, A237593, A240542, A244050, A245092, A276112, A277437, A279286, A279385, A280919, A280223, A282131, A282197, A280295, A281012.
%K A299693 nonn,tabf
%O A299693 1,2
%A A299693 _Omar E. Pol_, Feb 19 2018