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

0 votes
0 answers
135 views

An estimate of a sum

I'm looking for an estimate of this sum $\sum_{n\leq x} \frac{\mu^2(n)}{\varphi(n)}$ where $\mu$ is the Möbius function and $\varphi$ the Euler's totient function. Thanks a lot.
4 votes
1 answer
277 views

Rough numbers in short interval

A positive integer $n$ is called $k$-rough if all of the prime factors of $n$ strictly exceed $k$. For $k$ fixed and $n$ large, what's the shortest interval $[n,n+t]$ that contains a $k$-rough number …