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%I #7 Jan 08 2019 19:06:58
%S 1,1,1,1,3,1,1,5,2,1,9,7,2,1,11,8,2,1,17,19,10,2,1,21,25,14,3,1,27,37,
%T 24,6,1,31,42,26,6,1,41,73,68,32,6,1,45,79,72,33,6,1,57,124,151,105,
%U 39,6,1,63,138,167,114,41,6,1,71,159,192,128,44,6,1,79
%N Irregular triangle read by rows where T(n,k) is the number of pairwise coprime k-subsets of {1,...,n}, 1 <= k <= A036234(n), where a single number is not considered to be pairwise coprime unless it is equal to 1.
%e Triangle begins:
%e 1
%e 1 1
%e 1 3 1
%e 1 5 2
%e 1 9 7 2
%e 1 11 8 2
%e 1 17 19 10 2
%e 1 21 25 14 3
%e 1 27 37 24 6
%e 1 31 42 26 6
%e 1 41 73 68 32 6
%e 1 45 79 72 33 6
%e 1 57 124 151 105 39 6
%e 1 63 138 167 114 41 6
%e 1 71 159 192 128 44 6
%e 1 79 183 228 157 56 8
%t Table[Length[Select[Subsets[Range[n],{k}],CoprimeQ@@#&]],{n,16},{k,PrimePi[n]+1}]
%Y Except for the k = 1 column, same as A186974.
%Y Row sums are A320426.
%Y Second column is A015614.
%Y Cf. A051424, A084422, A085945, A187106, A276187, A320423, A320430, A320435.
%K nonn,tabf
%O 1,5
%A _Gus Wiseman_, Jan 08 2019
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