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 A365910 #31 Sep 25 2023 08:44:42
%S A365910 1,5,15,18,35,42
%N A365910 Minimum number of parts in a partition of all 4-subsets of an n-element set such that the intersection of any two subsets from the same part has size at most 1.
%C A365910 a(n) >= binomial(n-2,2).
%C A365910 a(n) >= binomial(n,4) / A004037(n).
%C A365910 For n >= 7, a(n) <= (3*n-11) * (n-4).
%H A365910 ArtOfProblemSolving et al., <a href="https://mathoverflow.net/q/363026">What is the best way to partition the 4-subsets of {1,2,3,...,n}?</a>, MathOverflow, 2020.
%H A365910 ArtOfProblemSolving et al., <a href="https://math.stackexchange.com/q/3717109">What is the best way to partition the 4-subsets of {1,2,3,...,n}?</a>, Mathematics StackExchange, 2020.
%o A365910 (Sage) def A365910(n): return Graph([Subsets(n,4), lambda u,v: u!=v and len(u&v)>1]).chromatic_number()
%Y A365910 Cf. A004037.
%K A365910 nonn,hard,more
%O A365910 4,2
%A A365910 _Max Alekseyev_, Sep 23 2023