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$2$-adic valuations and sum of divisor function

Consider the sum of $k^{th}$-power of divisors of $n$, denoted $$\sigma_k(n)=\sum_{d\vert n}d^k.$$ Let $\nu_p(x)$ stand for the $p$-adic valuation of the integer $x$. The following appears to be ...
T. Amdeberhan's user avatar
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Are there infinitely many $k$ for which $\frac{\sigma(k)}{k}=n^p$ and $p$ is an odd prime? [closed]

I would like to know if there are infinitely many $k$ for which $$\sigma(k)/k=n^p$$ such that $m=k{n}^{p-1}$ with $m,n>0$ and $p$ is an odd prime? Note: $\sigma(\frac{m}{{n}^{p-1}})$ is the sum of ...
zeraoulia rafik's user avatar