A068063 Maximum cardinality of a nondividing subset of {1, 2, ..., n}.

0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8

Offset: 0

Author

David Wasserman, Feb 15 2002

Keywords

• more
• nonn

Comments

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

Examples

			a(65) = 8 because 8 is the maximal cardinality of a nondividing subset of {1, 2, ..., 65}.  Two different subsets have cardinality 8:
{36,40,48,49,53,61,64,65}, {30,44,45,49,50,59,64,65}.
		

Links

• Eric Weisstein's World of Mathematics, Nondividing Set.

Crossrefs

Cf. A051014, A187489.

Extensions

a(41)-a(65) from Alois P. Heinz, Mar 10 2011