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%I #41 Mar 11 2014 01:34:21
%S 1,3,5,7,1,9,1,11,3,13,3,15,5,17,5,1,19,7,1,21,7,1,23,9,3,25,9,3,27,
%T 11,3,29,11,5,31,13,5,1,33,13,5,1,35,15,7,1,37,15,7,1,39,17,7,3,41,17,
%U 9,3,43,19,9,3,45,19,9,3,47,21,11,5,49,21,11,5,1
%N Triangle read by rows T(n,k), n>=1, k>=1, where T(n,k) is the sum of the divisors d of n with min(d, n/d) = k.
%C Column k lists the odd numbers repeated k times starting in row k^2.
%C 1 together with the first differences of the row sums give the divisor function A000005.
%C T(n,k) is also the total number of divisors of all positive integers <= n on the edges of k-th triangle in the diagram of divisors (see link section). See also A212119.
%H Omar E. Pol, , <a href="http://www.polprimos.com/imagenespub/poldiv04.jpg">Diagram of divisors, figure 1</a>, <a href="http://www.polprimos.com/imagenespub/poldiv05.jpg">figure 2</a>
%F T(n,k) = Sum_{j=1..n) A212119(j,k).
%e Written as an irregular triangle the sequence begins:
%e 1;
%e 3;
%e 5;
%e 7, 1;
%e 9, 1;
%e 11, 3;
%e 13, 3;
%e 15, 5;
%e 17, 5, 1;
%e 19, 7, 1;
%e 21, 7, 1;
%e 23, 9, 3;
%e 25, 9, 3;
%e 27, 11, 3;
%e 29, 11, 5;
%e 31, 13, 5, 1;
%e 33, 13, 5, 1;
%e 35, 15, 7, 1;
%e 37, 15, 7, 1;
%e 39, 17, 7, 3;
%e 41, 17, 9, 3;
%e 43, 19, 9, 3;
%e 45, 19, 9, 3;
%e 47, 21, 11, 5;
%e 49, 21, 11, 5, 1;
%Y Row sums give A006218, n >= 1.
%Y Columns (1-5): A005408, A109613, A130823, A129756, A130497.
%Y Cf. A000005, A027750, A010766, A147861, A163100, A212119.
%K nonn,tabf
%O 1,2
%A _Omar E. Pol_, Jul 02 2012
%E Definition changed by _Franklin T. Adams-Watters_, Jul 12 2012
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