This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A358370 #7 Nov 13 2022 12:27:25 %S A358370 0,0,0,1,1,1,1,2,1,2,2,3,2,3,3,4,3,4,3,5,3,5,4,6,5,6,4,7,5,7,5,8,6,8, %T A358370 7,9,6,9,6,10,7,10,7,11,9,11,8,12,8,12,9,13,9,13,11,14,9,14,10,15,10, %U A358370 15,10,16,13,16,11,17,12,17,12,18,12,18,15,19,14 %N A358370 a(n) is the size of the largest 3-independent set in the cyclic group Zn. %H A358370 Béla Bajnok, <a href="https://arxiv.org/abs/2211.01890">Additive Combinatorics in Groups and Geometric Combinatorics on Spheres</a>, arXiv:2211.01890 [math.NT], 2022. See p. 4. %H A358370 Béla Bajnok and Imre Ruzsa, <a href="https://www.emis.de/journals/INTEGERS/papers/d2/d2.pdf">The independence number of a subset of an abelian group</a>. Integers, 3 (2003), Paper A2. See p. 5. %F A358370 a(n) = floor(n/4) if n is even, a(n) = (1 + 1/p)*n/6 if n is odd with smallest prime divisor p congruent 5 mod 6, and a(n) = floor(n/6) otherwise. %t A358370 b[n_]:=Min[Intersection[Divisors[n], Select[Prime[Range[PrimePi[n]]], Mod[#, 6]==5 &]]]; a[n_]:=If[EvenQ[n], Floor[n/4], If[IntegerQ[b[n]], (1+1/b[n])n/6, Floor[n/6]]]; Array[a,80] %Y A358370 Cf. A002265, A007528, A027750, A152467. %K A358370 nonn,easy %O A358370 1,8 %A A358370 _Stefano Spezia_, Nov 12 2022