# Linked Questions

10 questions linked to/from Bound the error in estimating a relative totient function

**20**

votes

**6**answers

4k views

### Erik Westzynthius's cool upper bound argument: update?

Version 2 of this writeup is
available, and includes a newer and simple upper bound thanks to
MathOverflow 88777 as
well as indirect references to future writeups. Details of further work
...

**11**

votes

**2**answers

1k views

### distribution of coprime integers

Let $0 < a < 1$ be fixed, and integer $n$ tends to infinity. It is not hard to show that the number of integers $k$ coprime to $n$ such that $1\leq k\leq an$ asymtotically equals $(a+o(1))\...

**6**

votes

**1**answer

657 views

### When does Merten's product theorem accurately estimate the number of coprimes in an interval?

Assume an arbitrary $x$ and let $z$ be smaller than $y$, where $y$ is the length of the interval $[x,x+y]$. What I would like to know is:
Let $W(z)=\prod_{p\leq z}\left(1-\frac{1}{p}\right)$. For ...

**1**

vote

**4**answers

1k views

### Distribution of composite numbers

I have moved this question to math.stackexchange.com. People who are interested in this question can discuss at :https://math.stackexchange.com/questions/1272431/distribution-of-composite-numbers
...

**4**

votes

**1**answer

373 views

### References to proofs of upper and lower bounds on the number of coprimes in an interval?

On the first page of the article "When the sieve works", the authors present upper and lower bounds for $S(T,T+x;\mathcal{E})$; the number of integers in the interval $(T,T+x]$ that are coprime to all ...

**-3**

votes

**2**answers

484 views

### The number of totatives to the nth primorial, in an interval shorter than the nth primorial

(The notation of this question will be improved over the next few days, sorry for the lack of clarity at the moment.)
Can, and if so when can, we determine the amount of natural numbers which are ...

**2**

votes

**1**answer

176 views

### Bounds for relative totient function for small values

Define $\phi(n,x)= \sum_{m\leq x,\gcd(m,n)=1} 1$, the number of elements in the interval $[1,x]$ that is relatively prime to $n$. $\omega(n)$ is the number of distinct prime factors of $n$.
It's not ...

**6**

votes

**0**answers

312 views

### Should I expect to see numbers this smooth?

I have a sequence $N_k$ of numbers whose growth I wish to determine, or at least
approximate nicely. When I look at the ratios of consecutive members,
I find some interesting simplifications ...

**1**

vote

**1**answer

311 views

### Euler's Totient Function [duplicate]

Let $\phi(\cdot)$ be the Euler totient function, and let $n=p_1^{k_1}\cdots p_s^{k_s}$ be the prime factorization of $n\in \mathbb{N}$. The well-known Euler's product formula states that $\phi(n)=n(1-\...

**0**

votes

**2**answers

185 views

### Results regarding the relative-totient function

Let $\Lambda(x,n)$ be the the number of totatives of $x$ which are less than or equal to $n$, and $\Phi(x)$ be Euler's totient function.
For now assume $x>n$.
Is there a general formula for $\...