A274531 Irregular triangle read by rows: T(n,k) = sum of the elements of the k-th row of the absolute difference table of the divisors of n.

1, 3, 1, 4, 2, 7, 3, 1, 6, 4, 12, 5, 2, 2, 8, 6, 15, 7, 3, 1, 13, 8, 4, 18, 9, 4, 0, 12, 10, 28, 11, 5, 4, 3, 1, 14, 12, 24, 13, 6, 2, 24, 14, 8, 8, 31, 15, 7, 3, 1, 18, 16, 39, 17, 8, 10, 4, 4, 20, 18, 42, 19, 11, 4, 5, 1, 32, 20, 12, 8, 36, 21, 10, 6, 24, 22, 60, 23, 11, 10, 6, 5, 2, 2, 31, 24, 16, 42, 25, 12, 8

Offset

1,2

Comments

Row 2^k gives the first k+1 positive terms of A000225 in decreasing order, k >= 0.

If n is prime then row n contains only two terms: n+1 and n-1.

Note that this sequence is not the absolute values of A273261.

First differs from A273261 at a(41).

Links

Table of n, a(n) for n=1..91.

Example

Triangle begins:
1;
3, 1;
4, 2;
7, 3, 1;
6, 4;
12, 5, 2, 2;
8, 6;
15, 7, 3, 1;
13, 8, 4;
18, 9, 4, 0;
12, 10;
28, 11, 5, 4, 3, 1;
14, 12;
24, 13, 6, 2;
24, 14, 8, 8;
31, 15, 7, 3, 1;
18, 16;
39, 17, 8, 10, 4, 4;
20, 18;
42, 19, 11, 4, 5, 1;
32, 20, 12, 8;
36, 21, 10, 6;
24, 22;
60, 23, 11, 10, 6, 5, 2, 2;
31, 24, 16;
42, 25, 12, 8;
...
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 row sums give [39, 17, 8, 10, 4, 4] which is also the 18th row of the irregular triangle.

Mathematica

Map[Total, #, {2}] &@ Table[NestWhileList[Abs@ Differences@ # &, #, Length@ # > 1 &] &@ Divisors@ n, {n, 26}] // Flatten (* Michael De Vlieger, Jun 27 2016 *)

Crossrefs

Row lengths give A000005. Column 1 is A000203. Right border gives A187203. Row sums give A187215.

Cf. A000225, A273104, A273261, A274532, A274533.

Sequence in context: A234930 A351887 A273261 * A365434 A115659 A067060

Adjacent sequences: A274528 A274529 A274530 * A274532 A274533 A274534

Keyword

nonn,tabf

Author

Omar E. Pol, Jun 27 2016

Status

approved