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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}.
10
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
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
Row sums give: A051014.
Cf. A068063.
Sequence in context: A220484 A174066 A089178 * A355145 A116599 A138121
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Mar 10 2011
STATUS
approved