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A273104
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Absolute difference table of the divisors of the positive integers.
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5
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1, 1, 2, 1, 1, 3, 2, 1, 2, 4, 1, 2, 1, 1, 5, 4, 1, 2, 3, 6, 1, 1, 3, 0, 2, 2, 1, 7, 6, 1, 2, 4, 8, 1, 2, 4, 1, 2, 1, 1, 3, 9, 2, 6, 4, 1, 2, 5, 10, 1, 3, 5, 2, 2, 0, 1, 11, 10, 1, 2, 3, 4, 6, 12, 1, 1, 1, 2, 6, 0, 0, 1, 4, 0, 1, 3, 1, 2, 1, 1, 13, 12, 1, 2, 7, 14, 1, 5, 7, 4, 2, 2, 1, 3, 5, 15, 2, 2, 10, 0, 8, 8
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OFFSET
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1,3
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COMMENTS
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This is an irregular tetrahedron T(n,j,k) read by rows in which the slice n lists the elements of the rows of the absolute difference triangle of the divisors of n (including the divisors of n).
The first row of the slice n is also the n-th row of the triangle A027750.
The bottom entry of the slice n is A187203(n).
The sum of the elements of the slice n is A187215(n).
For another version see A273102 from which differs at a(92).
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LINKS
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EXAMPLE
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For n = 18 the divisors of 18 are 1, 2, 3, 6, 9, 18, so the absolute difference triangle of the divisors of 18 is
1 . 2 . 3 . 6 . 9 . 18
. 1 . 1 . 3 . 3 . 9
. . 0 . 2 . 0 . 6
. . . 2 . 2 . 6
. . . . 0 . 4
. . . . . 4
and the 18th slice is
1, 2, 3, 6, 9, 18;
1, 1, 3, 3, 9;
0, 2, 0, 6;
2, 2, 6;
0, 4;
4;
The tetrahedron begins:
1;
1, 2;
1;
1, 3;
2;
1, 2, 4;
1, 2;
1;
...
This is also an irregular triangle T(n,r) read by rows in which row n lists the absolute difference triangle of the divisors of n flattened.
Triangle begins:
1;
1, 2, 1;
1, 3, 2;
1, 2, 4, 1, 2, 1;
...
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MATHEMATICA
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Table[Drop[FixedPointList[Abs@ Differences@ # &, Divisors@ n], -2], {n, 15}] // Flatten (* Michael De Vlieger, May 16 2016 *)
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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