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Results tagged with perfect-numbers
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user 37555
A perfect number is a positive integer that is equal to the sum of its proper positive divisors.
11
votes
Accepted
Is there an odd integer $x < 105$ for which it is known that $x \nmid N$, if $N$ is an odd p...
No, such a result would be a major breakthrough regarding our knowledge on odd perfect numbers.
A few years ago there was some confusion, since due to careless reading and citing of the article "Eve …
3
votes
Is $\liminf \frac{\sigma_{k}(({2}^{m-1})({2^m-1}))}{\phi_{k}(({2}^{m-1})({2^m-1}))}$ finite ...
The problem is probably beyond current knowledge. It is well possible that $\liminf\omega(2^m-1)=\infty$, where $\omega(n)$ denotes the number of distinct prime divisors of $n$. If this was the case, …