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 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). 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS For n >= 1, the alternating row sums equal 0. LINKS Marcel K. Goh and Jonah Saks, Alternating-sum statistics for certain sets of integers, arXiv:2206.12535 [math.CO], 2022. EXAMPLE 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}. CROSSREFS Row sums give A084422. Cf. A000720, A036234, A186974, A320436. Sequence in context: A099573 A107430 A330885 * A255741 A132892 A174448 Adjacent sequences:  A355142 A355144 A355145 * A355147 A355149 A355150 KEYWORD nonn,tabf AUTHOR Marcel K. Goh, Jun 27 2022 STATUS approved

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Last modified August 14 17:12 EDT 2022. Contains 356122 sequences. (Running on oeis4.)