cp's OEIS Frontend

A187489 Irregular triangle T(n,k), n>=0, 0<=k<=A068063(n), read by rows: T(n,k) is the number of k-element nondividing subsets of {1, 2, ..., n}.

%I A187489 #17 Feb 16 2025 08:33:14
%S A187489 1,1,1,1,2,1,3,1,1,4,2,1,5,5,1,6,7,1,7,12,1,1,8,16,2,1,9,22,6,1,10,28,
%T A187489 12,1,1,11,37,22,2,1,12,43,31,3,1,13,54,49,6,1,14,64,70,10,1,15,75,99,
%U A187489 21,1,16,86,128,32,1,17,101,176,49,1,18,113,216,65,1,19,130,284,101
%N A187489 Irregular triangle T(n,k), n>=0, 0<=k<=A068063(n), read by rows: T(n,k) is the number of k-element nondividing subsets of {1, 2, ..., n}.
%C A187489 A set is called nondividing if no element divides the sum of any nonempty subset of the other elements.
%C A187489 T(n,k) = 0 for k>A068063(n). The triangle contains all positive values of T.
%H A187489 Alois P. Heinz, <a href="/A187489/b187489.txt">Rows n = 0..65, flattened</a>
%H A187489 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NondividingSet.html">Nondividing Set</a>
%e A187489 T(5,2) = 5, because there are 5 2-element nondividing subsets of {1,2,3,4,5}: {2,3}, {2,5}, {3,4}, {3,5}, {4,5}.  T(7,3) = 1: {4,6,7}.
%e A187489 Triangle T(n,k) begins:
%e A187489   1;
%e A187489   1, 1;
%e A187489   1, 2;
%e A187489   1, 3, 1;
%e A187489   1, 4, 2;
%e A187489   1, 5, 5;
%e A187489   1, 6, 7;
%e A187489   1, 7, 12, 1;
%e A187489   ...
%Y A187489 Columns k=0-8 give: A000012, A000027, A161664, A187490, A187491, A187492, A187493, A187494, A187550.
%Y A187489 Row sums give: A051014.
%Y A187489 Cf. A068063.
%K A187489 nonn,tabf
%O A187489 0,5
%A A187489 _Alois P. Heinz_, Mar 10 2011