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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.
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
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
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
Rightmost elements of rows give A187106.
Sequence in context: A370804 A251729 A187763 * A117670 A368253 A368260
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Mar 07 2011
STATUS
approved