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A187207 Irregular triangle read by rows in which row n lists the k=A000005(n) divisors of n in decreasing order, followed by the lists of their absolute differences up to order k-1.

%I A187207 #44 May 19 2016 04:33:19
%S A187207 1,2,1,1,3,1,2,4,2,1,2,1,1,5,1,4,6,3,2,1,3,1,1,2,0,2,7,1,6,8,4,2,1,4,
%T A187207 2,1,2,1,1,9,3,1,6,2,4,10,5,2,1,5,3,1,2,2,0,11,1,10,12,6,4,3,2,1,6,2,
%U A187207 1,1,1,4,1,0,0,3,1,0,2,1,1,13,1,12,14,7,2,1,7,5,1,2,4,2
%N A187207 Irregular triangle read by rows in which row n lists the k=A000005(n) divisors of n in decreasing order, followed by the lists of their absolute differences up to order k-1.
%H A187207 Alois P. Heinz, <a href="/A187207/b187207.txt">Rows n = 1..350, flattened</a>
%e A187207 Triangle begins:
%e A187207 [1];
%e A187207 [2, 1], [1];
%e A187207 [3, 1], [2];
%e A187207 [4, 2, 1], [2, 1], [1];
%e A187207 [5, 1], [4];
%e A187207 [6, 3, 2, 1], [3, 1, 1], [2, 0], [2];
%e A187207 [7, 1], [6];
%e A187207 [8, 4, 2, 1], [4, 2, 1], [2, 1], [1];
%e A187207 [9, 3, 1], [6, 2], [4];
%e A187207 [10, 5, 2, 1], [5, 3, 1], [2, 2], [0];
%e A187207 The terms of each row can form a regular triangle, for example row 10:
%e A187207 10, 5, 2, 1;
%e A187207 . 5, 3, 1;
%e A187207 .   2, 2;
%e A187207 .    0;
%p A187207 with(numtheory):
%p A187207 DD:= l-> [seq(abs(l[i]-l[i-1]), i=2..nops(l))]:
%p A187207 T:= proc(n) local l;
%p A187207       l:= sort([divisors(n)[]], `>`);
%p A187207       seq((DD@@i)(l)[], i=0..nops(l)-1);
%p A187207     end:
%p A187207 seq(T(n), n=1..20); # _Alois P. Heinz_, Aug 03 2011
%t A187207 row[n_] := (dd = Divisors[n]; Table[Differences[dd, k] // Reverse // Abs, {k, 0, Length[dd]-1}]); Table[row[n], {n, 1, 20}] // Flatten (* _Jean-François Alcover_, May 18 2016 *)
%Y A187207 Row n has length A184389(n) = A000217(A000005(n)). Row sums give A187215. Last terms of rows give A187203. Columns 1,2 give: A000027, A032742.
%Y A187207 Cf. A056538, A187205, A187208.
%K A187207 nonn,tabf,easy
%O A187207 1,2
%A A187207 _Omar E. Pol_, Aug 02 2011