Claims

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1990_06_01_yokota: Yokota's 1990 theorem that the number of integers that are sums of distinct unit fractions with denominators at most N is at least (1/2 − o(1)) log N, so is not o(log N); the first disproof, refereed, not cited by the site.

1997_12_01_yokota: Yokota's 1997 theorem that the number of integers that are sums of distinct unit fractions with denominators at most N lies between log N − 5 log log N and log N + 1, so is not o(log N); refereed, credited.

1999_12_01_croot: Croot's 1999 Main Theorem: every integer up to the harmonic sum minus (9/2 + o(1))(log log N)^2/log N is a sum of distinct unit fractions with denominators at most N, so F(N) is log N + O(1); refereed, credited.

2002_10_01_yokota: Yokota's 2002 Corollary 1: for large N the number of positive integers that are sums of distinct unit fractions with denominators at most N is at least the floor of H_N − (π²/3 + o(1))(log log N)²/log N; refereed, credited.

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