OFFSET
0,5
COMMENTS
A set is primitive if it does not contain distinct i and j such that i divides j.
For n >= 2, the alternating row sums equal -1.
LINKS
Marcel K. Goh and Jonah Saks, Alternating-sum statistics for certain sets of integers, arXiv:2206.12535 [math.CO], 2022.
FORMULA
Sum_{k=1..ceiling(n/2)} k * T(n,k) = A087077(n). - Alois P. Heinz, Jun 24 2022
EXAMPLE
Triangle T(n,k) begins:
n/k 0 1 2 3 4 5 6 7 8 9 10 11 12
0 1
1 1 1
2 1 2
3 1 3 1
4 1 4 2
5 1 5 5 2
6 1 6 7 3
7 1 7 12 10 3
8 1 8 16 15 5
9 1 9 22 26 13 2
10 1 10 28 38 22 4
11 1 11 37 66 60 26 4
12 1 12 43 80 76 35 6
...
For n=6 and k=3 the T(6,3) = 3 primitive sets are {2,3,5}, {3,4,5}, and {4,5,6}.
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Marcel K. Goh, Jun 20 2022
STATUS
approved