A038372 Largest subset of integers [ 1...n ] such that no member divides two others.

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

Offset

1,2

References

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

Links

Table of n, a(n) for n=1..44.

Formula

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

Example

{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.

Crossrefs

Sequence in context: A032509 A322042 A004523 * A121930 A020909 A075357

Adjacent sequences: A038369 A038370 A038371 * A038373 A038374 A038375

Keyword

nonn

Author

John W. Layman

Extensions

More terms and additional comments from Jud McCranie, Jan 17 2001

Status

approved