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.

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, 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, 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

Offset: 1

Author

Omar E. Pol, Aug 02 2011

Keywords

• nonn
• tabf
• easy

Examples

			Triangle begins:
[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, 2, 1], [2, 1], [1];
[9, 3, 1], [6, 2], [4];
[10, 5, 2, 1], [5, 3, 1], [2, 2], [0];
The terms of each row can form a regular triangle, for example row 10:
10, 5, 2, 1;
. 5, 3, 1;
.   2, 2;
.    0;
		

Links

• Alois P. Heinz, Rows n = 1..350, flattened

Crossrefs

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.

Cf. A056538, A187205, A187208.

Programs

Maple

with(numtheory):
DD:= l-> [seq(abs(l[i]-l[i-1]), i=2..nops(l))]:
T:= proc(n) local l;
      l:= sort([divisors(n)[]], `>`);
      seq((DD@@i)(l)[], i=0..nops(l)-1);
    end:
seq(T(n), n=1..20); # Alois P. Heinz, Aug 03 2011

Mathematica

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 *)