Newbetuts

Is $\limsup_n \frac{\sigma(n)}{n \log p(n)} <\infty$, where $p(n)$ is the greatest prime factor of $n$ and $\sigma(n)=\sum_{d | n} d$?

Relationship between different L-functions

What is known about these arithmetical functions?

Number of distinct prime divisors of an integer $n$ is $O(\log n/\log\log n)$

What is known about the minimal number $f(n)$ of geometric progressions needed to cover $\{1,2,\ldots,n\}$, as a function of $n$?

Explicit formula for floor(x)?

How do we prove $p_n\sim n\log(n\log(n))$ from the Prime Number Theorem?

Riemann Hypothesis and the prime counting function

M and n are positive integers such that $2^n - 3^m > 0$. Prove (or disprove) that $2^n - 3^m \geqslant 2^{n-m}-1$.

For what $t$ does $\lim\limits_{n \to \infty} \frac{1}{n^t} \sum\limits_{k=1}^n \text{prime}(k)$ converge?

Generating function for the divisor function

Arithmetical Functions Sum, $\sum\limits_{d|n}\sigma(d)\phi(\frac{n}{d})$ and $\sum\limits_{d|n}\tau(d)\phi(\frac{n}{d})$

Modular transformations of $\eta(\tau)$

How do I prove $\sum_{n \leq x} \frac{\mu (n)}{n} \log^2{\frac{x}{n}}=2\log{x}+O(1)$? Can I use Abel summation?

Squares in $(\operatorname{rad}(1)^2+1)\cdot(\operatorname{rad}(2)^2+1)\ldots(\operatorname{rad}(n)^2+1)$

Derivative of the Riemann zeta function for $Re(s)>0$.

Bounds on a sum of gcd's

New posts in analytic-number-theory

Asymptotic behaviour of $\sum_{p\leq x} \frac{1}{p^2}$

Sum of Dirichlet's Character Over Divisors of Natural Number

Fourier Series involving the Jacobi Symbol

Is $\limsup_n \frac{\sigma(n)}{n \log p(n)} <\infty$, where $p(n)$ is the greatest prime factor of $n$ and $\sigma(n)=\sum_{d | n} d$?

Relationship between different L-functions

What is known about these arithmetical functions?

Number of distinct prime divisors of an integer $n$ is $O(\log n/\log\log n)$

What is known about the minimal number $f(n)$ of geometric progressions needed to cover $\{1,2,\ldots,n\}$, as a function of $n$?

Explicit formula for floor(x)?

How do we prove $p_n\sim n\log(n\log(n))$ from the Prime Number Theorem?

Riemann Hypothesis and the prime counting function

M and n are positive integers such that $2^n - 3^m > 0$. Prove (or disprove) that $2^n - 3^m \geqslant 2^{n-m}-1$.

For what $t$ does $\lim\limits_{n \to \infty} \frac{1}{n^t} \sum\limits_{k=1}^n \text{prime}(k)$ converge?

Generating function for the divisor function

Arithmetical Functions Sum, $\sum\limits_{d|n}\sigma(d)\phi(\frac{n}{d})$ and $\sum\limits_{d|n}\tau(d)\phi(\frac{n}{d})$

Modular transformations of $\eta(\tau)$

How do I prove $\sum_{n \leq x} \frac{\mu (n)}{n} \log^2{\frac{x}{n}}=2\log{x}+O(1)$? Can I use Abel summation?

Squares in $(\operatorname{rad}(1)^2+1)\cdot(\operatorname{rad}(2)^2+1)\ldots(\operatorname{rad}(n)^2+1)$

Derivative of the Riemann zeta function for $Re(s)>0$.

Bounds on a sum of gcd's