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A229944 Triangle read by rows in which T(2n-2,k) = n/k if k divides n and n/k > sqrt(n), otherwise 0, for n >= 2. Also T(2n-1,k) = k if k divides n, otherwise 0, for n >= 1. Row lengths are the same row lengths of A229940.

%I A229944 #10 Nov 13 2021 05:50:15
%S A229944 1,2,1,3,1,4,1,2,5,0,1,0,6,3,1,2,7,0,1,0,8,4,1,2,9,0,1,0,3,10,5,0,1,2,
%T A229944 0,11,0,0,1,0,0,12,6,4,1,2,3,13,0,0,1,0,0,14,7,0,1,2,0,15,0,5,1,0,3,
%U A229944 16,8,0,1,2,0,4,17,0,0,0,1,0,0,0,18,9,6,0,1,2,3,0
%N A229944 Triangle read by rows in which T(2n-2,k) = n/k if k divides n and n/k > sqrt(n), otherwise 0, for n >= 2. Also T(2n-1,k) = k if k divides n, otherwise 0, for n >= 1. Row lengths are the same row lengths of A229940.
%C A229944 The positive terms are also the divisors associated with the exposed endpoints of the toothpick structure of A229950 which is related to A000005. Note that the exposed toothpick endpoints are equivalent to the vertices of the graph mentioned in A229940. See link section.
%H A229944 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/poldiv13.jpg">Illustration of initial terms of the divisor function (A000005)</a>, see the third picture.
%e A229944 Triangle begins:
%e A229944 1;
%e A229944 2;
%e A229944 1;
%e A229944 3;
%e A229944 1;
%e A229944 4;
%e A229944 1,  2;
%e A229944 5,  0;
%e A229944 1,  0;
%e A229944 6,  3;
%e A229944 1,  2;
%e A229944 7,  0;
%e A229944 1,  0;
%e A229944 8,  4;
%e A229944 1,  2;
%e A229944 9,  0;
%e A229944 1,  0,  3;
%e A229944 10, 5,  0;
%e A229944 1,  2,  0;
%e A229944 11, 0,  0;
%e A229944 1,  0,  0;
%e A229944 12, 6,  4;
%e A229944 1,  2,  3;
%e A229944 13, 0,  0;
%e A229944 1,  0,  0;
%e A229944 14, 7,  0;
%e A229944 1,  2,  0;
%e A229944 15, 0,  5;
%e A229944 1,  0,  3;
%e A229944 16, 8,  0;
%e A229944 1,  2,  0,  4;
%e A229944 ...
%Y A229944 Cf. A000005, A000203, A229940, A229942, A229950, A229951.
%K A229944 nonn,tabf
%O A229944 1,2
%A A229944 _Omar E. Pol_, Oct 05 2013