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.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..10607 (rows 1..3500 of triangle, flattened).
EXAMPLE
Triangle begins:
1;
3;
1, 3;
3;
1, 5;
6;
1, 7;
3;
1, 3, 0;
3, 5;
1, 11;
6;
1, 13;
3, 7;
1, 8, 0;
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 the sum of noncomposite numbers is 1 + 2 + 3 = 6, so T(78,1) = 6. In the second 2-dense sublist the sum of noncomposite numbers is 13, so T(78,2) = 13.
MATHEMATICA
A390609row[n_] := Map[Total[Select[#, !CompositeQ[#] &]] &, Split[Divisors[n], #2 <= 2*# &]];
Array[A390609row, 50] (* Paolo Xausa, Nov 21 2025 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Nov 12 2025
STATUS
approved
