Intereting Posts

Is my proof valid? Integration of logarithmic function.
How do I prove that any unit fraction can be represented as the sum of two other distinct unit fractions?
Finding the derivatives of inverse functions at given point of c
Are there an equal number of positive and negative numbers?
Value of $\lim_{n\to \infty}\frac{1^n+2^n+\cdots+(n-1)^n}{n^n}$
Riemann Hypothesis and the prime counting function
Analytic Vectors (Nelson's Theorem)
Partial sums of exponential series
About the (non-trivial, this time) zeroes of an almost-periodic function
Total number of divisors is a prime
Is there an irrational number containing only $0$'s and $1$'s with continued fraction entries less than $10$?
A bounded subset in $\mathbb R^2$ which is “nowhere convex”?
Riemannian metric in the projective space
Topologist's sine curve is connected
How do you explain the concept of logarithm to a five year old?

Is $\displaystyle\sum\frac1{p^{1+ 1/p}}$ divergent? How can we prove that it is divergent or convergent in analytic number theory?

I know what bound of the n-th prime number is, and that its order is $n\log(n)$.

Maybe we can use the divergence of $\displaystyle\sum\frac1{n^{1+ 1/n}}$ to show that. I’m not sure that $\displaystyle\sum\frac1{n^{1+ 1/n}}$ is divergent, but I think it is.

So would you please help me with this ? Can you help me in finding a proof for it ?

Thank you very much, friends.

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- Evaluating $\sum\limits_{n=1}^{\infty} \frac{1}{n\operatorname{ GPF}(n)}$, where $\operatorname{ GPF}(n)$ is the greatest prime factor
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- Proving the functional equation $\theta (x) = x^{-\frac{1}{2}} \theta (x^{-1})$ from the Poisson summation formula

This is a great question. But you can show that

$$\frac 1{p^{1+1/p}} > \frac 1{2p}$$

since $2^p >p$, and thus your series diverges.

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- A question about an $n$-dimensional subspace of $\mathbb{F}^{S}$.
- Archimedean Property – The use of the property in basic real anaysis proofs
- 4-Color Theorem on Surfaces
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