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Erdős Problem #309 — Integer values of finite unit-fraction subset sums

About 46 years old · traced to

How many integers can be represented as ∑k=1Nϵk/k\sum_{k=1}^N\epsilon_k/k with each ϵk∈{0,1}\epsilon_k\in\{0,1\}? Is the number o(log⁡N)o(\log N)?

References

Primary source

P. Erdős and R. L. Graham, Old and new problems and results in combinatorial number theory, Monographies de L'Enseignement Mathématique 28 (1980).

Additional references

P. Erdős and R. L. Graham, Old and new problems and results in combinatorial number theory, Monographies de L'Enseignement Mathématique 28 (1980).

number-theoryunit-fractions
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