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A274533
Irregular triangle read by rows: T(n,k) = sum of the elements of the k-th column of the absolute difference table of the divisors of n.
2
1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 4, 5, 6, 6, 7, 7, 4, 6, 8, 8, 7, 9, 9, 4, 7, 10, 10, 11, 11, 4, 6, 8, 10, 12, 12, 13, 13, 8, 9, 14, 14, 11, 13, 15, 15, 5, 8, 12, 16, 16, 17, 17, 8, 11, 12, 15, 18, 18, 19, 19, 7, 10, 10, 15, 20, 20, 13, 17, 21, 21, 16, 13, 22, 22, 23, 23, 6, 7, 10, 12, 16, 20, 24, 24, 21, 25, 25
OFFSET
1,2
COMMENTS
If n is prime then row n is [n, n].
It appears that the last two terms of the n-th row are [n, n], n > 1.
Note that this sequence is not the absolute values of A273263.
First differs from A273263 at a(38).
EXAMPLE
Triangle begins:
1;
2, 2;
3, 3;
3, 4, 4;
5, 5;
4, 5, 6, 6;
7, 7;
4, 6, 8, 8;
7, 9, 9;
4, 7, 10, 10;
11, 11;
4, 6, 8, 10, 12, 12;
13, 13;
8, 9, 14, 14;
11, 13, 15, 15;
5, 8, 12, 16, 16;
17, 17;
8, 11, 12, 15, 18, 18;
19, 19;
7, 10, 10, 15, 20, 20;
13, 17, 21, 21;
16, 13, 22, 22;
23, 23;
6, 7, 10, 12, 16, 20, 24, 24;
21, 25, 25;
20, 15, 26, 26;
...
For n = 18 the divisors of 18 are 1, 2, 3, 6, 9, 18, and the absolute difference triangle of the divisors is
1, 2, 3, 6, 9, 18;
1, 1, 3, 3, 9;
0, 2, 0, 6;
2, 2, 6;
0, 4;
4;
The column sums give [8, 11, 12, 15, 18, 18] which is also the 18th row of the irregular triangle.
MATHEMATICA
Table[Total /@ Table[#[[m - k + 1, -k]], {m, Length@ #, 1, -1}, {k, m}] &@ NestWhileList[Abs@ Differences@ # &, Divisors@ n, Length@ # > 1 &], {n, 25}] // Flatten (* Michael De Vlieger, Jun 29 2016 *)
CROSSREFS
Row lengths give A000005. Right border gives A000027. Row sums give A187215.
Sequence in context: A219519 A330393 A273263 * A163127 A077113 A143796
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Jun 29 2016
STATUS
approved