

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.


11



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
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OFFSET

1,2


COMMENTS

T(n,k) = T(n,k1) 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=110 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: A159685 A251729 A187763 * A117670 A181695 A322291
Adjacent sequences: A187259 A187260 A187261 * A187263 A187264 A187265


KEYWORD

nonn,tabf


AUTHOR

Alois P. Heinz, Mar 07 2011


STATUS

approved



