# Tagged Questions

224 views

### Is there a closed form expression for the sum of all the proper divisors of an integer?

I have already found a summation formula here: http://math.stackexchange.com/a/22723, and also a very interesting recursive formula here: http://math.stackexchange.com/a/22744. Any ideas on how to ...
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### Does sequences related to function for $lcm(1,2,3 \cdots n)$ exists?

This just came out of curiosity let $$L(n)=lcm(1,2,3 \cdots n)$$ and I know that we can write this with the help of some product involving primes and all . But what I am interested is in Does ...
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### Summing up numbers from the continued fraction of $e ^ \pi$ and $\pi ^e$

I don't remember it well ,but it was around 5-6 years ago , I was 8 and I had found this new interest - continued fractions .I used to play with their terms sum them up and thought of getting ...
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### Proof of a striking identity of Tito Piezas III

In the q series blog of Tito Piezas here . He gives a very striking relation I am wondering on how to prove that ?
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### Closed form for a special recursion?

Does the recurrence relation $$a(n+1) = a(n)^2 + 1,\quad a(1)=1,$$ have a closed form solution? I have tried hard to find it, but failed. Any ideas ? I am particular interested in prime ...
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### Does $E^2 \; ( E \approx 1.2640847\ldots)$ equal $D \approx 1.5979102\ldots$?

Does $E^2=D$? Where $E$ is a constant used in the closed form of the Sylvester Sequence (see: Closed form formula and asymptotics) and $D$ is a constant for the closed formula of the sequence A007018 ...
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### Find a number $A$ so that $\lfloor A^{3^n} \rfloor$ are always odd

Find a number $A$ so that (1) $\lfloor A^{3^n} \rfloor$ is always odd for $n\geq 1$;($\lfloor x \rfloor$ is the largest integer not greater than $x.$) (2) $A>1$ and $A^{3^n}$ is never an ...
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### Is any closed-form representation known for the sum $\sum\limits_{n=1}^{\infty}\frac{\mu(n)\log n}{n^2}$?

Is any closed-form representation known for the sum $\sum\limits_{n=1}^{\infty}\frac{\mu(n)\log n}{n^2}$, where $\mu(n)$ is the Möbius $\mu$-function?
The nth term of the Fibonacci series is given by $F_{n}$=$\Big\lfloor\frac{\phi^{n}}{\sqrt{5}}+\frac{1}{2}\Big\rfloor$ How do you get the following expression for n from this? ...