A390496 Irregular triangle read by rows: T(n,k) is the largest number in the k-th 2-dense sublist of divisors of n, with n >= 1, k >= 1.

1, 2, 1, 3, 4, 1, 5, 6, 1, 7, 8, 1, 3, 9, 2, 10, 1, 11, 12, 1, 13, 2, 14, 1, 5, 15, 16, 1, 17, 18, 1, 19, 20, 1, 3, 7, 21, 2, 22, 1, 23, 24, 1, 5, 25, 2, 26, 1, 3, 9, 27, 28, 1, 29, 30, 1, 31, 32, 1, 3, 11, 33, 2, 34, 1, 7, 35, 36, 1, 37, 2, 38, 1, 3, 13, 39, 40, 1, 41, 42, 1, 43, 4, 44, 1, 15, 45, 2, 46, 1, 47, 48

Offset

1,2

Comments

In a sublist of divisors of n the terms are in increasing order and two adjacent terms are the same two adjacent terms in the list of divisors of n.

The 2-dense sublists of divisors of n are the maximal sublists whose terms increase by a factor of at most 2.

At least for the first 1000 rows the row lengths give A237271.

The column 1 first differs from both A193267 and A327832 at its 28th term.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10607 (rows 1..3500 of triangle, flattened).

Example

Triangle begins:
   1;
   2;
   1,  3;
   4;
   1,  5;
   6;
   1,  7;
   8;
   1,  3,  9;
   2, 10;
   1, 11;
  12;
   1, 13;
   2, 14;
   1,  5, 15;
  16;
  ...
For n = 10 the list of divisors of 10 is [1, 2, 5, 10]. There are two 2-dense sublists of divisors of 10, they are [1, 2] and [5, 10]. In the first 2-dense sublist the largest number is 2, so T(10,1) = 2. In the second 2-dense sublist the largest number is 10, so T(10,2) = 10.

Mathematica

A390496row[n_] := Map[Max, Split[Divisors[n], #2 <= 2*# &]];
Array[A390496row, 50] (* Paolo Xausa, Nov 23 2025 *)

Crossrefs

Right border gives A000027.

Cf. A027750, A174973 (2-dense numbers), A237271, A379288, A384149, A384222, A384225, A384226, A386604, A386989, A386992, A387030, A389592, A389761, A389762, A390443, A390494, A390495, A390609, A390610.

Cf. A193267, A327832.

Sequence in context: A224823 A372387 A395917 * A078753 A119443 A209413

Adjacent sequences: A390493 A390494 A390495 * A390497 A390498 A390499

Keyword

nonn,tabf

Author

Omar E. Pol, Nov 15 2025

Status

approved