1,11

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.

Paolo Xausa, Table of n, a(n) for n = 1..12242 (rows 1..4000 of triangle, flattened).

T(n,k) = A384222(n,k) - A389761(n,k).

Triangle begins:

0;

0;

0, 0;

1;

0, 0;

1;

0, 0;

2;

0, 0, 1;

0, 1;

0, 0;

3;

0, 0;

0, 1;

0, 0, 1;

3;

...

For n = 78 the list of divisors of 78 is [1, 2, 3, 6, 13, 26, 39, 78]. There are two 2-dense sublists of divisors of 78, they are [1, 2, 3, 6] and [13, 26, 39, 78]. In the first 2-dense sublist there is only one composite number [6], so T(78,1) = 1. In the second 2-dense sublist there are three composite numbers [26, 39, 78], so T(78,2) = 3.

A389762row[n_] := Map[Count[#, _?CompositeQ] &, Split[Divisors[n], #2 <= 2*# &]];

Array[A389762row, 50] (* Paolo Xausa, Oct 21 2025 *)

Row sums give A055212.

Cf. A002808, A027750, A174973 (2-dense numbers), A237271, A379288, A384225, A386992, A387030, A389761.

Sequence in context: A340999 A119395 A087476 * A307505 A035162 A121454

Adjacent sequences: A389759 A389760 A389761 * A389763 A389764 A389765

nonn,tabf

Omar E. Pol, Oct 14 2025

approved