A360285 Triangle read by rows: T(n,k) is the number of subsets of {1,...,n} of cardinality k in which no two elements are coprime; n >= 0, 0 <= k <= floor(n/2) + [n=1].

1, 1, 1, 1, 2, 1, 3, 1, 4, 1, 1, 5, 1, 1, 6, 4, 1, 1, 7, 4, 1, 1, 8, 7, 4, 1, 1, 9, 9, 5, 1, 1, 10, 14, 11, 5, 1, 1, 11, 14, 11, 5, 1, 1, 12, 21, 24, 16, 6, 1, 1, 13, 21, 24, 16, 6, 1, 1, 14, 28, 39, 36, 21, 7, 1, 1, 15, 34, 48, 41, 22, 7, 1, 1, 16, 41, 69, 76, 57, 28, 8, 1

Offset: 0

Author

Marcel K. Goh, Feb 01 2023

Keywords

• nonn
• tabf

Examples

			Triangle T(n,k) begins:
   n/k 0  1  2  3  4 5 6
   0   1
   1   1  1
   2   1  2
   3   1  3
   4   1  4  1
   5   1  5  1
   6   1  6  4  1
   7   1  7  4  1
   8   1  8  7  4  1
   9   1  9  9  5  1
  10   1 10 14 11  5 1
  11   1 11 14 11  5 1
  12   1 12 21 24 16 6 1
  ...
For n=8 and k=3 the T(8,3)=4 sets are {2,4,6}, {2,4,8}, {2,6,8}, and {4,6,8}.
		

Links

• Marcel K. Goh and Jonah Saks, Alternating-sum statistics for certain sets of integers, arXiv:2206.12535 [math.CO], 2022.

Crossrefs

Cf. A056171, A355146.