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.

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, 9, 36, 73, 97, 103, 10, 41, 83, 109, 115, 11, 52, 125, 193, 225, 231, 12, 57, 136, 208, 241, 247, 13, 70, 194, 345, 450, 489, 495, 14, 77, 215, 382, 496, 537, 543

Offset

1,2

Comments

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.

Links

Alois P. Heinz, Rows n = 1..200, flattened

Formula

T(n,k) = Sum_{i=1..n,j=1..k} A186972(i,j).

T(n,k) = Sum_{j=1..k} A186974(n,j).

T(n,k) = Sum_{i=1..n} A186975(i,k).

Example

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}.
Irregular Triangle T(n,k) begins:
  1;
  2,  3;
  3,  6,  7;
  4,  9, 11;
  5, 14, 21, 23;
  6, 17, 25, 27;
  7, 24, 43, 53, 55;

Crossrefs

Columns k=1-10 give: A000027, A187263, A187264, A187265, A187266, A187267, A187268, A187269, A187270, A187271.

Rightmost elements of rows give A187106.

Cf. A036234, A186972, A186974, A186975.

Sequence in context: A370804 A251729 A187763 * A117670 A368253 A368260

Adjacent sequences: A187259 A187260 A187261 * A187263 A187264 A187265

Keyword

nonn,tabf

Author

Alois P. Heinz, Mar 07 2011

Status

approved