# Tagged Questions

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### Is the Green-Tao theorem a consequence of the Euler's theorem?

The Erdős-Turán conjecture states that If $A\subset\mathbb{N}$ is such that $$\sum_{n\in A} \frac{1}{n} = \infty,$$ then $A$ contains arithmetic progressions of any given length. I'm ...
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### Liouville function and PNT

The Big Omega function is defined as the number on non-distinct prime factors of an integer. I.e. $\Omega (2^a3^b...p^z)=a+b+...+z$, and the Liouville function is defined as ...
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### On a constant defined by Ramanujan.

In the second letter to Hardy Ramanujan writes about the number of prime numbers less than $n$ there he writes. Here this constant $\mu$ facinated me . What is its closed form? and How to compute ...
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### Prime number theorem and how many primes are close to $x$ for sufficiently large $n$

The prime number theorem states: $$\lim_{x-> \infty}{\frac{\pi(x)}{\frac{x}{ln(x)}}} = 1$$ I was trying to get a better understanding on the intuition on that statement and more importantly, I ...
Determine all primes numbers $p$ such that $$p \sum_{k=0}^{n}\frac{1}{2k+1} \in N$$ for a given positive number $n$