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A272121 Absolute difference table of the divisors of the positive integers (with every table read by antidiagonals downwards). 5
1, 1, 2, 1, 1, 3, 2, 1, 2, 1, 4, 2, 1, 1, 5, 4, 1, 2, 1, 3, 1, 0, 6, 3, 2, 2, 1, 7, 6, 1, 2, 1, 4, 2, 1, 8, 4, 2, 1, 1, 3, 2, 9, 6, 4, 1, 2, 1, 5, 3, 2, 10, 5, 2, 0, 1, 11, 10, 1, 2, 1, 3, 1, 0, 4, 1, 0, 0, 6, 2, 1, 1, 1, 12, 6, 4, 3, 2, 1, 1, 13, 12, 1, 2, 1, 7, 5, 4, 14, 7, 2, 2, 1, 3, 2, 5, 2, 0, 15, 10, 8, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
This is an irregular tetrahedron T(n,j,k) in which the slice n lists the elements of the j-th antidiagonal of the absolute difference triangle of 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 number of elements in the n-th slice is A000217(A000005(n)) = A184389(n).
The sum of the elements of the n-th slice is A187215(n).
If n is a power of 2 the antidiagonals are also the divisors of the powers of 2 from 1 to n in decreasing order, for example if n = 8 the finite sequence of andiagonals is [1], [2, 1], [4, 2, 1], [8, 4, 2, 1].
First differs from A273135 at a(92).
Note that this sequence is not the absolute values of A273135. For example a(135) = 0 and A273135(135) = 4.
LINKS
EXAMPLE
The tables of the first nine positive integers are
1; 1, 2; 1, 3; 1, 2, 4; 1, 5; 1, 2, 3, 6; 1, 7; 1, 2, 4, 8; 1, 3, 9;
. 1; 2; 1, 2; 4; 1, 1, 3; 6; 1, 2, 4; 2, 6;
. 1; 0, 2; 1, 2; 4;
. 2; 1;
.
For n = 18 the absolute difference table 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;
This table read by antidiagonals downwards gives the finite subsequence [1], [2, 1], [3, 1, 0], [6, 3, 2, 2], [9, 3, 0, 2, 0], [18, 9, 6, 6, 4, 4].
MATHEMATICA
Table[Table[#[[m - k + 1, k]], {m, Length@ #}, {k, m, 1, -1}] &@ NestWhileList[Abs@ Differences@ # &, Divisors@ n, Length@ # > 1 &], {n, 15}] // Flatten (* Michael De Vlieger, Jun 26 2016 *)
CROSSREFS
Sequence in context: A316831 A355737 A112380 * A273135 A165162 A125106
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, May 18 2016
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)