%I
%S 1,2,0,2,1,0,3,0,0,0,2,2,1,0,0,4,0,0,0,0,0,2,2,0,1,0,0,0,4,0,2,0,0,0,
%T 0,0,3,3,0,0,1,0,0,0,0,4,0,0,0,0,0,0,0,0,0,2,2,2,2,0,1,0,0,0,0,0,6,0,
%U 0,0,0,0,0,0,0,0,0,0,2,4,0,0,0,0,1,0
%N Square array T(n,k) read by antidiagonals in which column k lists the number of divisors of n that are divisible by k.
%C It appears that the sequence formed by starting with an initial set of k1 zeros followed by the members of A000005, with k1 zeros between every one of them, can be defined as "the number of divisors of n that are divisible by k", (k >= 1). For example: if k = 1 we have A000005 by definition; if k = 2 we have A183063. Note that if k >= 3 the sequences are not included in the OEIS because the usual OEIS policy is not to include sequences with interspersed zeros. A183063 is an exception.
%C It appears that the illustration of initial terms of column k can be represented by a general diagram in which the period of the smallest curve is 2*k, hence the distance between consecutive two nodes is equal to k. (For k = 1 see the link.)
%C Row sums = A007425.  _Geoffrey Critzer_, Feb 07 2015
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/poldiv01.jpg">Illustration of initial terms of column 1</a>
%F Dirichlet generating function of column k: zeta(s)*Sum_{n>=1}1/(k*n)^s.  _Geoffrey Critzer_, Feb 07 2015
%e Array begins:
%e 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
%e 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
%e 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
%e 3, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,...
%e 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,...
%e 4, 2, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0,...
%e 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,...
%e 4, 3, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0,...
%e 3, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0,...
%e 4, 2, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0,...
%e 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,...
%e 6, 4, 3, 2, 0, 2, 0, 0, 0, 0, 0, 1,...
%t (* returns square array *)
%t nn = 20; Transpose[Table[Table[DirichletConvolve[1, Floor[n/k]  Floor[(n  1)/k], n, m], {m, 1,nn}], {k, 1, nn}]] // Grid (* _Geoffrey Critzer_, Feb 07 2015 *)
%Y Columns (1,2): A000005, A183063.
%Y Cf. A051731, A127170.
%K nonn,tabl
%O 1,2
%A _Omar E. Pol_, Oct 18 2011
