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}.

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, 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, 21, 1, 16, 86, 128, 32, 1, 17, 101, 176, 49, 1, 18, 113, 216, 65, 1, 19, 130, 284, 101

Offset

0,5

Comments

A set is called nondividing if no element divides the sum of any nonempty subset of the other elements.

T(n,k) = 0 for k>A068063(n). The triangle contains all positive values of T.

Links

Alois P. Heinz, Rows n = 0..65, flattened

Eric Weisstein's World of Mathematics, Nondividing Set

Example

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}.
Triangle T(n,k) begins:
  1;
  1, 1;
  1, 2;
  1, 3, 1;
  1, 4, 2;
  1, 5, 5;
  1, 6, 7;
  1, 7, 12, 1;
  ...

Crossrefs

Columns k=0-8 give: A000012, A000027, A161664, A187490, A187491, A187492, A187493, A187494, A187550.

Row sums give: A051014.

Cf. A068063.

Sequence in context: A220484 A174066 A089178 * A355145 A116599 A138121

Adjacent sequences: A187486 A187487 A187488 * A187490 A187491 A187492

Keyword

nonn,tabf

Author

Alois P. Heinz, Mar 10 2011

Status

approved