A229944 - OEIS

%I #10 Nov 13 2021 05:50:15

%S 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 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 16,8,0,1,2,0,4,17,0,0,0,1,0,0,0,18,9,6,0,1,2,3,0

%N 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 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 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 Triangle begins:

%e 1;

%e 2;

%e 1;

%e 3;

%e 1;

%e 4;

%e 1,  2;

%e 5,  0;

%e 1,  0;

%e 6,  3;

%e 1,  2;

%e 7,  0;

%e 1,  0;

%e 8,  4;

%e 1,  2;

%e 9,  0;

%e 1,  0,  3;

%e 10, 5,  0;

%e 1,  2,  0;

%e 11, 0,  0;

%e 1,  0,  0;

%e 12, 6,  4;

%e 1,  2,  3;

%e 13, 0,  0;

%e 1,  0,  0;

%e 14, 7,  0;

%e 1,  2,  0;

%e 15, 0,  5;

%e 1,  0,  3;

%e 16, 8,  0;

%e 1,  2,  0,  4;

%e ...

%Y Cf. A000005, A000203, A229940, A229942, A229950, A229951.

%K nonn,tabf

%O 1,2

%A _Omar E. Pol_, Oct 05 2013