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

Author

Omar E. Pol, Jun 27 2016

Keywords

• nonn
• tabf

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).

Examples

			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.
		

Crossrefs

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

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

Programs

Mathematica

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