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A187207
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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.
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5
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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
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history;
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OFFSET
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1,2
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LINKS
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Alois P. Heinz, Rows n = 1..350, flattened
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EXAMPLE
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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;
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MAPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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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
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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Omar E. Pol, Aug 02 2011
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STATUS
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approved
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