A057561 Size of the largest set encompassing no {x, 2x, 3x} contained in D(n) = the first n 3-smooth numbers {1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, ...} (A003586).

1, 2, 2, 3, 4, 5, 5, 6, 7, 7, 8, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 16, 17, 17, 18, 18, 19, 20, 21, 21, 22, 22, 23, 24, 25, 25, 26, 26, 27, 28, 29, 30, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 36, 37, 38, 39, 39, 40, 41, 42, 42, 42, 43, 44, 45, 45, 46, 47

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

This is the weakly triple-free analog of A157271.

A094708(n) = n - a(n).

Position of first n gives A004059(n).

Graham paper erroneously has a(30)=20. - Sean A. Irvine, Nov 18 2015

Examples

			A set for a(30) is {1, 2, 6, 8, 9, 12, 16, 27, 36, 48, 54, 64, 72, 96, 128, 162, 216, 243, 256, 288, 324}. - _Sean A. Irvine_, Oct 26 2015
		

References

• R. L. Graham et al., On extremal density theorems for linear forms, pp. 103-109 of H. Zassenhaus, editor, Number Theory and Algebra. Academic Press, NY, 1977.

Links

• F. Chung, P. Erdős, R. Graham, On sparse sets hitting linear forms, Proc. Number Theory for the Millennium, 1, pp. 257-272, 2000.
• Steven R. Finch, Triple-Free Sets of Integers [From Steven Finch, Apr 20 2019]
• R. L. Graham et al., On extremal density theorems for linear forms, pp. 103-109 of H. Zassenhaus, editor, Number Theory and Algebra. Academic Press, NY, 1977.

Crossrefs

Cf. A004059, A094708, A003586, A157271.

Extensions

Edited by Steven Finch, Feb 25 2009

Revised by N. J. A. Sloane, Jun 13 2012

a(30) corrected and more terms from Sean A. Irvine, Oct 26 2015