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%I #50 Nov 30 2025 14:16:48
%S 1,2,3,4,5,5,6,7,8,9,10,10,11,12,13,14,15,16,17,18,19,20,21,21,22,23,
%T 24,25,26,26,27,28,29,30,31,32,33,34,35,35,36,36,37,38,39,40,41,41,42,
%U 43,44,45,46,47,48,48,49,50,51,52,53,54,55,56,57,57,58,59
%N a(n) is the maximum size of a subset S of {1,...,n} such that there are no solutions to 1/a = 1/b + 1/c for distinct a,b,c in S.
%C Erdős has conjectured that a(n) = (1/2 + o(1))*n.
%C Further estimates can be found on the Erdős Problems site.
%H Sharvil Kesarwani, <a href="/A390395/b390395.txt">Table of n, a(n) for n = 1..731</a> (first 658 terms from Chai Wah Wu)
%H Thomas Bloom, <a href="https://www.erdosproblems.com/302">Problem 302</a>, Erdős Problems.
%H P. Erdős and R. Graham, <a href="https://mathweb.ucsd.edu/~ronspubs/80_11_number_theory.pdf">Old and new problems and results in combinatorial number theory</a>, Monographies de L'Enseignement Mathématique (1980).
%H Erdős problems database contributors, <a href="https://github.com/teorth/erdosproblems/issues/152">Issue #152</a> linking Erdős problems to the OEIS.
%H Husnain Raza, <a href="https://raw.githubusercontent.com/epistemologist/OEIS_Sequences/refs/heads/main/A390395/gen_terms.py">Python program</a>.
%e For n = 12, the largest subset of {1,...,12} not containing the subsets {2, 3, 6}, {3, 4, 12}, {4, 12, 6} has size 10.
%o (Python)
%o from itertools import combinations
%o def A390395(n):
%o s, t = [], set()
%o for b in range(1,n+1):
%o for c in range(b+1,n+1):
%o a, r = divmod(b*c,b+c)
%o if not r:
%o s.append({a,b,c})
%o t |= {a,b,c}
%o l = len(t)
%o for i in range(l,-1,-1):
%o for d in combinations(t,i):
%o if not any(x.issubset(d) for x in s):
%o return n-l+i # _Chai Wah Wu_, Nov 19 2025
%o (Python)
%o from pysat.examples.hitman import Hitman
%o def A390395(n):
%o h = Hitman(solver='g42')
%o for b in range(1,n+1):
%o for c in range(b+1,n+1):
%o a, r = divmod(b*c,b+c)
%o if not r:
%o h.hit([a,b,c])
%o return n-len(h.get()) # _Chai Wah Wu_, Nov 21 2025
%K nonn
%O 1,2
%A _Husnain Raza_, Nov 04 2025
%E a(40)-a(68) from _Chai Wah Wu_, Nov 19 2025