A379461 Irregular triangle read by rows in which row n lists the divisors m of n such that there is a divisor d of n with d < m < 2*d, or 0 if such divisors do not exist.

0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 4, 6, 0, 0, 5, 0, 0, 3, 9, 0, 5, 0, 0, 0, 3, 4, 6, 8, 12, 0, 0, 0, 7, 0, 3, 5, 6, 10, 15, 0, 0, 0, 0, 7, 3, 4, 6, 9, 12, 18, 0, 0, 0, 5, 8, 10, 0, 3, 7, 21, 0, 0, 5, 9, 15, 0, 0, 3, 4, 6, 8, 12, 16, 24, 0, 0, 0, 0, 0, 3, 9, 27, 0

Offset: 1

Author

Omar E. Pol, Dec 23 2024

Keywords

• nonn
• tabf

Comments

The number of positive terms in row n is A174903(n).

The indices of the rows that contain a zero give A174905.

The indices of the rows that contain positive integers give A005279.

The positive integers in the n-th row are the missing divisors of n in the n-th row of A379374.

The odd integers in the n-th row are the missing odd divisors of n in the n-th row of A379288.

Examples

			Triangle begins:
  0;
  0;
  0;
  0;
  0;
  3;
  0;
  0;
  0;
  0;
  0;
  3, 4, 6;
  0;
  0;
  5;
  0;
  0;
  3, 9;
  0;
  5;
  ...
From _Omar E. Pol_, Apr 19 2025: (Start)
For n = 12 there are three divisors m of 12 such that there is a divisor d of 12 with d < m < 2*d. Those divisors are 3, 4 and 6 as shown below:
   d  <  m  <  2*d
--------------------
   1            2
   2     3      4
   3     4      6
   4     6      8
   6           12
  12           24
.
So the 12th row of the triangle is [3, 4, 6]. (End)
		

Crossrefs

Cf. A005279, A027750, A174903, A174905, A182469, A237271, A379288, A379374, A379379, A379384, A383209.

Programs

Mathematica

row[n_] := Module[{d = Partition[Divisors[n], 2, 1], e}, e = Select[d, #[[2]] < 2*#[[1]] &][[;; , 2]]; If[e == {}, {0}, e]]; Table[row[n], {n, 1, 55}] // Flatten (* Amiram Eldar, Dec 23 2024 *)

Extensions

More terms from Amiram Eldar, Dec 23 2024

Name changed by Omar E. Pol, Feb 05 2025