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 A386820 #15 Aug 08 2025 00:38:27
%S A386820 0,0,0,0,0,4,4,4,4,4,4,6,6,6,9,9,9,11,11,11,14,14,14
%N A386820 a(n) is the size of largest subset of {1, 1/2, ..., 1/n} that can be partitioned into two parts, the sum of elements of which are equal.
%H A386820 Art of Problem Solving, <a href="https://artofproblemsolving.com/community/c6h2112349p15298955">2020 GQMO Problem 4</a>, which shows that a(n) >= 2*n/5 for sufficiently large n.
%H A386820 Vincent Jugé, <a href="/A386820/a386820.pdf">Proof that a(n) > c*n for all real numbers c < 1 and sufficiently large n</a>
%F A386820 a(n) = a(n-1) if n/k = p is a prime and p > A001008(k).
%e A386820 For a(6) = 4, the set {1, 1/2, 1/3, 1/6} is chosen because 1 = 1/2 + 1/3 + 1/6.
%e A386820 The two parts for a(18) = 11 are 1 + 1/5 + 1/6 + 1/15 = 1/2 + 1/3 + 1/4 + 1/9 + 1/10 + 1/12 + 1/18.
%e A386820 The two parts for a(20) = 11 are 1 + 1/9 + 1/10 + 1/15 + 1/18 = 1/2 + 1/3 + 1/5 + 1/6 + 1/12 + 1/20.
%Y A386820 Cf. A001008, A098181.
%K A386820 nonn,more
%O A386820 1,6
%A A386820 _Yifan Xie_, Aug 03 2025