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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

14 votes
2 answers
922 views

How many divisors of $n$ are below $n^{1/3}$?

I am trying to bound a function that includes $\sum\limits_{\substack{d < n^{1/3} \\ d \mid n}} 1$. Is there an upper bound known for this sum, either in general or in terms of $\sum\limits_{\substack …