A273104 - OEIS

%I #27 Apr 02 2017 17:11:55

%S 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,

%T 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,

%U 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

%N Absolute difference table of the divisors of the positive integers.

%C 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).

%C The first row of the slice n is also the n-th row of the triangle A027750.

%C The bottom entry of the slice n is A187203(n).

%C The sum of the elements of the slice n is A187215(n).

%C For another version see A273102 from which differs at a(92).

%e 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

%e 1 . 2 . 3 . 6 . 9 . 18

%e . 1 . 1 . 3 . 3 . 9

%e . . 0 . 2 . 0 . 6

%e . . . 2 . 2 . 6

%e . . . . 0 . 4

%e . . . . . 4

%e and the 18th slice is

%e 1, 2, 3, 6, 9, 18;

%e 1, 1, 3, 3, 9;

%e 0, 2, 0, 6;

%e 2, 2, 6;

%e 0, 4;

%e 4;

%e The tetrahedron begins:

%e 1;

%e 1, 2;

%e 1;

%e 1, 3;

%e 2;

%e 1, 2, 4;

%e 1, 2;

%e 1;

%e ...

%e 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.

%e Row lengths are the terms of A184389. Row sums give A187215.

%e Triangle begins:

%e 1;

%e 1, 2, 1;

%e 1, 3, 2;

%e 1, 2, 4, 1, 2, 1;

%e ...

%t Table[Drop[FixedPointList[Abs@ Differences@ # &, Divisors@ n], -2], {n, 15}] // Flatten (* _Michael De Vlieger_, May 16 2016 *)

%Y Cf. A027750, A184389, A187202-A187205, A187207-A187209, A187215, A273102.

%K nonn,tabf

%O 1,3

%A _Omar E. Pol_, May 15 2016