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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. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

EXAMPLE

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;

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-Fran├žois Alcover, May 18 2016 *)

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.

Sequence in context: A181087 A029288 A238899 * A050117 A241187 A212822

Adjacent sequences:  A187204 A187205 A187206 * A187208 A187209 A187210

KEYWORD

nonn,tabf,easy

AUTHOR

Omar E. Pol, Aug 02 2011

STATUS

approved

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Last modified August 18 20:02 EDT 2019. Contains 326109 sequences. (Running on oeis4.)