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.

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).

Links

Table of n, a(n) for n=1..87.

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.

Cf. A187203, A272121, A273132, A273104, A273137, A273263, A274531, A274532.

Sequence in context: A219519 A330393 A273263 * A163127 A077113 A143796

Adjacent sequences: A274530 A274531 A274532 * A274534 A274535 A274536

Keyword

nonn,tabf

Author

Omar E. Pol, Jun 29 2016

Status

approved