Newbetuts

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?

Prove that $p^j q^i$ cannot be a perfect number for $p, q$ odd, distinct primes.

Can an odd perfect number be divisible by $5313$?

How to show that all even perfect numbers are obtained via Mersenne primes?

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

Discussion on even and odd perfect numbers.

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

Does the following lower bound improve on $I(q^k) + I(n^2) > 3 - \frac{q-2}{q(q-1)}$, where $q^k n^2$ is an odd perfect number? - Part II

Can an odd perfect number be divisible by $165$?

Can this bound for the abundancy index of $n$ be improved, given that $q^k n^2$ is an odd perfect number with $k=1$?

If $N = q^k n^2$ is an odd perfect number and $n < q^{k+1}$, does it follow that $k > 1$?

Help with "A Simpler Dense Proof regarding the Abundancy Index."

On odd perfect numbers and a GCD - Part V

When $p$ is an odd prime, is $(p+2)/p$ an outlaw or an index?

New posts in perfect-numbers

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

Has it been conjectured that all $k$-multiperfect numbers are multiples of $k$?

Combinatorial interpretation of Euclid's form for even perfect numbers

Applications of Perfect Numbers

On odd perfect numbers $p^k m^2$ with special prime $p$ satisfying $m^2 - p^k = 2^r t$ - Part II

Elementary Proof of No Odd Perfect Numbers [closed]

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?

Prove that $p^j q^i$ cannot be a perfect number for $p, q$ odd, distinct primes.

Can an odd perfect number be divisible by $5313$?

How to show that all even perfect numbers are obtained via Mersenne primes?

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

Discussion on even and odd perfect numbers.

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

Does the following lower bound improve on $I(q^k) + I(n^2) > 3 - \frac{q-2}{q(q-1)}$, where $q^k n^2$ is an odd perfect number? - Part II

Can an odd perfect number be divisible by $165$?

Can this bound for the abundancy index of $n$ be improved, given that $q^k n^2$ is an odd perfect number with $k=1$?

If $N = q^k n^2$ is an odd perfect number and $n < q^{k+1}$, does it follow that $k > 1$?

Help with "A Simpler Dense Proof regarding the Abundancy Index."

On odd perfect numbers and a GCD - Part V

When $p$ is an odd prime, is $(p+2)/p$ an outlaw or an index?