Alexander Kalmynin's user avatar
Alexander Kalmynin's user avatar
Alexander Kalmynin's user avatar
Alexander Kalmynin
  • Member for 6 years
  • Last seen this week
23 votes

Does the average primeness of natural numbers tend to zero?

22 votes
Accepted

The constant $e$ represented by an infinite series

22 votes

Find all positive integers $n$ such that $n+\tau{(n)}=2\varphi{(n)}$

22 votes
Accepted

Number of 1's in binary expansion of $a_n = \frac{2^{\varphi(3^n)}-1}{3^n}$

20 votes
Accepted

Under a condition, $\frac{1}{b } = \sum_{n=1}^{\infty}\frac{1}{a_{n}}$ will never happen

19 votes
Accepted

Are there any papers about this observation of the distribution of the zeros of the zeta function?

18 votes
Accepted

Singularities of power series

14 votes

Probability that product is a perfect square

14 votes

Non trivial zeros of Riemann zeta function

13 votes

A sum involving Euler totient function

13 votes

Sum of the reciprocals of radicals

13 votes
Accepted

on a strange character sum

11 votes

Are there more than two rational solutions to $a^b= b^a$?

10 votes

Must Mersenne numbers be divisible by arbitrary large primes with exponent one?

10 votes
Accepted

$3\times 3$ magic squares consisting of entries of a dense set $D\subseteq \mathbb{N}$

9 votes
Accepted

Covering the primes with pairs of consecutive integers

8 votes
Accepted

Prove $ \sum_{i=0}^{2a+1} {2a+1 \choose i} B_{2a+1-i} [ (n+1)^i+(-n)^i ] =0 $ for Bernoulli numbers $B_{n}$

8 votes
Accepted

Eisenstein series $E_4(z)$ and $E_6(z)$ algebraically independent over $\mathbb{C}$

8 votes
Accepted

Condition for $8p+1$ divides $(2^p+1)/3$?

8 votes
Accepted

Are there infinitely many nonzero Euler quotients $a(n)=\frac{2^{\phi(n)}-1}{n} \bmod n$?

7 votes
Accepted

Factorising n! fitting $x^\frac{n}{k}$

7 votes
Accepted

Fourier transform of periodic distributions

7 votes
Accepted

Given the integral. What's the relation between $I_{n+1}(t)$ and $I_n(t)$?

7 votes
Accepted

Asymptotics of $\operatorname{lcm} ((2-1), (3-1), (5-1), (7-1), (11-1), \dotsc, p_n-1 )$

7 votes
Accepted

A conjecture concerning the equation $\sigma\left(\square\right)=\text{prime}$

7 votes
Accepted

Is this Goldbach conjecture related quantity equal to the number of Goldbach decompositions up to a bounded quantity?

6 votes
Accepted

A generalization Bertrand's postulate

6 votes
Accepted

Is it true that $\det\big[\sin 2\pi\frac{(j-k)^2}p\big]_{1\le j,k\le p-1}=-\frac{p^{(p-1)/2}}{2^{p-1}}$ for each prime $p\equiv3\pmod4$?

6 votes

Counting squares modulo $p$ that are also prime in an interval

6 votes
Accepted

Estimating a sum over prime numbers