A194881 A number of sum-free sets related to fractional parts of multiples of a rational number in the range 1/3 to 2/3.

2, 3, 6, 8, 12, 15, 21, 25, 34, 38, 48, 54, 66, 72, 84, 92, 108, 117, 135, 143, 161, 171, 193, 205, 225, 237, 264, 276, 304, 316, 346, 362, 392, 408, 432, 450, 486, 504, 540, 556, 596, 614, 656, 676, 712, 734, 780, 804, 846

Offset: 1

Author

R. J. Mathar, Sep 04 2011

Keywords

• nonn

Comments

Deserves a better title which mentions n in the sense that this is a sum-free set from a difference set with {1,....,n}.

Links

• Peter J. Cameron and Paul Erdős, Notes on sum-free and related sets, Combinat. Probabl. Comput. 8 (1&2) (1999), 95-107, Theorem 4.

Crossrefs

Cf. A000010, A195459, A372621.

Programs

Maple

A194881 := proc(n) 1+add(numtheory[phi](3*q),q=1..n)/2 ; end proc:
seq(A194881(n),n=1..80) ;

Mathematica

Accumulate[Table[EulerPhi[3*n], {n, 1, 60}]]/2 + 1 (* Amiram Eldar, May 08 2024 *)

Formula

a(n) = 1 + Sum_{j=1..n} A000010(3*j)/2.

a(n) ~ (27/(8*Pi^2)) * n^2. - Amiram Eldar, May 08 2024