query: Finding the closed form $\phi(n) / n^x$
positive_passages.docid: 28220
positive_passages.text: totient function series diverges?
negative_passages.docid: 65653
negative_passages.text: Find a closed form of the series $\sum_{n=0}^{\infty} n^2x^n$
negative_passages.docid: 87479
negative_passages.text: Closed form for $\sum_{k=0}^{n-p}\binom{n}{k}\binom{n}{p+k}$
negative_passages.docid: 121723
negative_passages.text: $\phi(n)=\frac{n}{2}$ if and only if $n=2^k$ for some positive integer k
negative_passages.docid: 157711
negative_passages.text: Number Theory: Prove that $m | \phi(a^m - 1)$
negative_passages.docid: 104982
negative_passages.text: Determine $\phi(2^{399}+1)$
negative_passages.docid: 139307
negative_passages.text: Closed form expression for infinite series
negative_passages.docid: 138819
negative_passages.text: Prove that $\phi(n) \geq \sqrt{n}/2$
negative_passages.docid: 53263
negative_passages.text: Show $\sum\limits_{d|n}\phi(d) = n$.
negative_passages.docid: 136623
negative_passages.text: Hints/ Solution in finding a formula $\phi(n)$ for a binary square matrix
negative_passages.docid: 58972
negative_passages.text: Proof/Derivation of Closed form of Binomial Expression $\sum\limits_{k=0}^{2n}(-1)^k\binom{2n}{k}^2$
negative_passages.docid: 19914
negative_passages.text: Closed form for $\sum_{n=0}^{\infty} \binom{n+k}{k} x^n$ (Negative Binomial Theorem)
negative_passages.docid: 52951
negative_passages.text: Find all $n \in \mathbb{Z^+}$ such that $\phi(n)=4$
negative_passages.docid: 110275
negative_passages.text: Let $p>0$. Show the $\lim_{n\to\infty}(a^n/n^p)$ is equal to:
negative_passages.docid: 47753
negative_passages.text: Closed form of series with factorial-squared denominator?
negative_passages.docid: 39909
negative_passages.text: Getting a closed form from $\sum_{i=1}^{n-1} \sum_{j=i+1}^{n} \sum_{k=1}^{j} 1$
negative_passages.docid: 4530
negative_passages.text: For which natural numbers are $\phi(n)=2$?