The harmonic series diverges slowly, proportional to log n. The sum of the reciprocals of primes diverges very slowly, proportional to log log n. Is there an elegant integer sequence whose reciprocals diverge even more slowly? We are looking for a sequence that grows as n*(ln n)*(ln (ln n)) or something like that.
I don't consider floor(n ln n ln ln n) elegant.
Perhaps something related to disjoint-set union-find.
Reciprocals of Mersenne prime exponents? Sophie Germain primes?
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