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A187262 Irregular triangle T(n,k), n>=1, 1<=k<=A036234(n), read by rows: T(n,k) is the number of nonempty subsets of {1, 2, ..., n} having <=k pairwise coprime elements.

%I A187262 #15 Oct 04 2018 19:39:07
%S A187262 1,2,3,3,6,7,4,9,11,5,14,21,23,6,17,25,27,7,24,43,53,55,8,29,54,68,71,
%T A187262 9,36,73,97,103,10,41,83,109,115,11,52,125,193,225,231,12,57,136,208,
%U A187262 241,247,13,70,194,345,450,489,495,14,77,215,382,496,537,543
%N A187262 Irregular triangle T(n,k), n>=1, 1<=k<=A036234(n), read by rows: T(n,k) is the number of nonempty subsets of {1, 2, ..., n} having <=k pairwise coprime elements.
%C A187262 T(n,k) = T(n,k-1) for k>A036234(n).  The triangle contains all values of T up to the last element of each row that is different from its predecessor.
%H A187262 Alois P. Heinz, <a href="/A187262/b187262.txt">Rows n = 1..200, flattened</a>
%F A187262 T(n,k) = Sum_{i=1..n,j=1..k} A186972(i,j).
%F A187262 T(n,k) = Sum_{j=1..k} A186974(n,j).
%F A187262 T(n,k) = Sum_{i=1..n} A186975(i,k).
%e A187262 T(5,3) = 21 because there are 21 nonempty subsets of {1,2,3,4,5} having <=3 pairwise coprime elements: {1}, {2}, {3}, {4}, {5}, {1,2}, {1,3}, {1,4}, {1,5}, {2,3}, {2,5}, {3,4}, {3,5}, {4,5}, {1,2,3}, {1,2,5}, {1,3,4}, {1,3,5}, {1,4,5}, {2,3,5}, {3,4,5}.
%e A187262 Irregular Triangle T(n,k) begins:
%e A187262   1;
%e A187262   2,  3;
%e A187262   3,  6,  7;
%e A187262   4,  9, 11;
%e A187262   5, 14, 21, 23;
%e A187262   6, 17, 25, 27;
%e A187262   7, 24, 43, 53, 55;
%Y A187262 Columns k=1-10 give: A000027, A187263, A187264, A187265, A187266, A187267, A187268, A187269, A187270, A187271.
%Y A187262 Rightmost elements of rows give A187106.
%Y A187262 Cf. A036234, A186972, A186974, A186975.
%K A187262 nonn,tabf
%O A187262 1,2
%A A187262 _Alois P. Heinz_, Mar 07 2011