A355146 Triangle read by rows: T(n,k) is the number of subsets of {1,...,n} of cardinality k in which every pair of elements is coprime; n >= 0, 0 <= k <= A036234(n).

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 5, 2, 1, 5, 9, 7, 2, 1, 6, 11, 8, 2, 1, 7, 17, 19, 10, 2, 1, 8, 21, 25, 14, 3, 1, 9, 27, 37, 24, 6, 1, 10, 31, 42, 26, 6, 1, 11, 41, 73, 68, 32, 6, 1, 12, 45, 79, 72, 33, 6, 1, 13, 57, 124, 151, 105, 39, 6, 1, 14, 63, 138, 167, 114, 41, 6

Offset: 0

Author

Marcel K. Goh, Jun 27 2022

Keywords

• nonn
• tabf

Comments

For n >= 1, the alternating row sums equal 0.

Examples

			Triangle T(n,k) begins:
  n/k 0  1  2  3  4  5 6
  0   1
  1   1  1
  2   1  2  1
  3   1  3  3  1
  4   1  4  5  2
  5   1  5  9  7  2
  6   1  6 11  8  2
  7   1  7 17 19 10  2
  8   1  8 21 25 14  3
  9   1  9 27 37 24  6
  10  1 10 31 42 26  6
  11  1 11 41 73 68 32 6
  12  1 12 45 79 72 33 6
  ...
For n=8 and k=5 the T(8,5)=3 sets are {1,2,3,5,7}, {1,3,4,5,7}, and {1,3,5,7,8}.
		

Links

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

Crossrefs

Row sums give A084422.

Cf. A000720, A036234, A186974, A320436.