Newbetuts

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

Identity with nested sum taken over divisors of $\gcd$'s

Can a composite number $n$ be the arithmetic mean of $\sigma(n)$ and $\varphi(n)$?

Is there an odd solution of $\varphi(n)+n=\sigma(n)$?

Interesting convergence in divisor sums up to $10^k$

What numerical lower bound on the index of an odd perfect number is implied by the results in F.-J. Chen and Y.-G. Chen's 2014 paper?

What's the sum of all the positive integral divisors of $540$?

When does $\gcd(m,\sigma(m^2))$ equal $\gcd(m^2,\sigma(m^2))$? What are the exceptions?

Evaluating the sum $\sum_{i=1}^n i^2\cdot\lfloor{\frac ni}\rfloor$

On the inequality $I(q^k)+I(n^2) \leq \frac{3q^{2k} + 2q^k + 1}{q^k (q^k + 1)}$ where $q^k n^2$ is an odd perfect number

Find the sum of reciprocals of divisors given the sum of divisors

For any positive integer $n$, show that $\sum_{d|n}\sigma(d) = \sum_{d|n}(n/d)\tau(d)$

How did Descartes come up with the spoof odd perfect number $198585576189$?

When is the sum of divisors a perfect square?

Are there infinitely many sets of relatively prime numbers with equal number and sum of divisors?

New posts in divisor-sum

Why can this cosine sum function show all primes less than $N^2$?

On odd perfect numbers $n$ and $\sigma\left(n^\lambda\right)$

Prove that $\sum_{n=1}^\infty \frac{\sigma_a(n)}{n^s}=\zeta(s)\zeta(s-a)$

The number of divisors of a number whose sum of divisors is a perfect square

Holomorphic Differentials on a non-singular curve.

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

Identity with nested sum taken over divisors of $\gcd$'s

Can a composite number $n$ be the arithmetic mean of $\sigma(n)$ and $\varphi(n)$?

Is there an odd solution of $\varphi(n)+n=\sigma(n)$?

Interesting convergence in divisor sums up to $10^k$

What numerical lower bound on the index of an odd perfect number is implied by the results in F.-J. Chen and Y.-G. Chen's 2014 paper?

What's the sum of all the positive integral divisors of $540$?

When does $\gcd(m,\sigma(m^2))$ equal $\gcd(m^2,\sigma(m^2))$? What are the exceptions?

Evaluating the sum $\sum_{i=1}^n i^2\cdot\lfloor{\frac ni}\rfloor$

On the inequality $I(q^k)+I(n^2) \leq \frac{3q^{2k} + 2q^k + 1}{q^k (q^k + 1)}$ where $q^k n^2$ is an odd perfect number

Find the sum of reciprocals of divisors given the sum of divisors

For any positive integer $n$, show that $\sum_{d|n}\sigma(d) = \sum_{d|n}(n/d)\tau(d)$

How did Descartes come up with the spoof odd perfect number $198585576189$?

When is the sum of divisors a perfect square?

Are there infinitely many sets of relatively prime numbers with equal number and sum of divisors?