cp's OEIS Frontend

A212119 Triangle read by rows T(n,k), n>=1, k>=1, where T(n,k) is the number of divisors d of n with min(d, n/d) = k.

%I A212119 #45 Dec 04 2013 17:47:58
%S A212119 1,2,2,2,1,2,0,2,2,2,0,2,2,2,0,1,2,2,0,2,0,0,2,2,2,2,0,0,2,2,0,2,0,2,
%T A212119 2,2,0,1,2,0,0,0,2,2,2,0,2,0,0,0,2,2,0,2,2,0,2,0,2,2,0,0,2,0,0,0,2,2,
%U A212119 2,2,2,0,0,0,1,2,2,0,0,0,2,0,2,0,0
%N A212119 Triangle read by rows T(n,k), n>=1, k>=1, where T(n,k) is the number of divisors d of n with min(d, n/d) = k.
%C A212119 Column k lists the numbers A040000: 1, 2, 2, 2, 2... interleaved with k-1 zeros, starting in row k^2.
%C A212119 The sum of row n gives A000005(n), the number of divisors of n.
%C A212119 T(n,k) is also the number of divisors of n on the edges of k-th triangle in the diagram of divisors (see link section). See also A212120.
%C A212119 It appears that there are only eight rows that do not contain zeros. The indices of these rows are 1, 2, 3, 4, 6, 8, 12, 24, the divisors of 24, see A018253. - _Omar E. Pol_, Dec 03 2013
%H A212119 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>
%H A212119 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/poldiv13.jpg">Illustration of initial terms and of row sums</a>
%e A212119 Row 10 gives 2, 2, 0 therefore the sums of row 10 is 2+2+0 = 4, the same as A000005(10), the number of divisors of 10.
%e A212119 Written as an irregular triangle the sequence begins:
%e A212119 1;
%e A212119 2;
%e A212119 2;
%e A212119 2, 1;
%e A212119 2, 0;
%e A212119 2, 2;
%e A212119 2, 0;
%e A212119 2, 2;
%e A212119 2, 0, 1;
%e A212119 2, 2, 0;
%e A212119 2, 0, 0;
%e A212119 2, 2, 2;
%e A212119 2, 0, 0;
%e A212119 2, 2, 0;
%e A212119 2, 0, 2;
%e A212119 2, 2, 0, 1;
%e A212119 2, 0, 0, 0;
%e A212119 2, 2, 2, 0;
%e A212119 2, 0, 0, 0;
%e A212119 2, 2, 0, 2;
%e A212119 2, 0, 2, 0;
%e A212119 2, 2, 0, 0;
%e A212119 2, 0, 0, 0;
%e A212119 2, 2, 2, 2;
%e A212119 2, 0, 0, 0, 1;
%Y A212119 Row sums give A000005. Column 1 is A040000. Column 2 gives the absolute values of A176742.
%Y A212119 Cf. A006218, A027750, A010766, A147861, A163100, A196020, A210959, A212120, A211343, A221645, A228812-A228814.
%K A212119 nonn,tabf
%O A212119 1,2
%A A212119 _Omar E. Pol_, Jul 02 2012
%E A212119 Definition changed by _Franklin T. Adams-Watters_, Jul 12 2012