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.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..12242 (rows 1..4000 of triangle, flattened).
EXAMPLE
Triangle begins:
1;
2;
1, 1;
2;
1, 1;
3;
1, 1;
2;
1, 1, 0;
2, 1;
1, 1;
3;
1, 1;
2, 1;
1, 2, 0;
2;
...
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 are three noncomposite numbers [1, 2, 3], so T(78,1) = 3. In the second 2-dense sublist there is only one noncomposite number [13], so T(78,2) = 1.
MATHEMATICA
A389761row[n_] := Map[Count[#, _?(!CompositeQ[#] &)] &, Split[Divisors[n], #2 <= 2*# &]];
Array[A389761row, 50] (* Paolo Xausa, Oct 21 2025 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Oct 14 2025
STATUS
approved
