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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 18 17:48 EDT 2022. Contains 353823 sequences. (Running on oeis4.)