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

1,2

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

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

Table of n, a(n) for n=1..69.

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.

Example

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

Crossrefs

Cf. A004059, A094708, A003586, A157271.

Sequence in context: A218445 A034137 A156351 * A064726 A274616 A257175

Adjacent sequences: A057558 A057559 A057560 * A057562 A057563 A057564

Keyword

nonn

Author

N. J. A. Sloane

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

Status

approved