A038372 - OEIS

%I #8 Mar 30 2012 18:34:53

%S 1,2,2,3,4,4,5,6,6,7,8,8,9,10,10,11,12,12,13,14,14,15,16,16,17,18,19,

%T 20,21,21,22,22,22,23,24,24,25,26,26,27,28,28,29,30

%N Largest subset of integers [ 1...n ] such that no member divides two others.

%D R. K. Guy, Unsolved Problems Number Theory, B24.

%F a(n) >= ceiling(2n/3). For large n, 0.6725n <= a(n) <= 0.6736n (see Guy).

%e {6,8-17,19-23,25-29} is the largest set of positive integers <= 29 such that none of them divides two of the others. The cardinality of the set is 21, so a(29)=21.

%K nonn

%O 1,2

%A _John W. Layman_

%E More terms and additional comments from _Jud McCranie_, Jan 17 2001