A. Shakov

collaborators

3 papers

math.NT2025

A $2$ -Regular Sequence That Counts The Divisors of $n^{2} + 1$

Anton Shakov

We introduce the $2$ -regular integer sequence A383066 $= (s (n))_{n \geq 1}$ , which begins $0, 1, 1, 2, 3, 3, 2, \dots$ . We prove that the number of occurrences of an integer $m \g…

math.GM2024

Infinite Primes From Integer Partitions

Anton Shakov

Ferrers diagrams are used to visually represent integer partitions. We describe a way to use Ferrers diagrams to uniquely represent integers in terms of their prime factors. This l…

math.NT2024

Polynomials whose divisors are enumerated by $S L_{2} (N_{0})$

Anton Shakov

We consider a certain left action by the monoid $S L_{2} (N_{0})$ on the set of divisor pairs $\mathcal{D}_f := \{ (m, n) \in \mathbf{N}_0 \times \mathbf{N}_0 : m \lvert f(n) \}…

A 2-Regular Sequence That Counts The Divisors of n2+1

Infinite Primes From Integer Partitions

Polynomials whose divisors are enumerated by SL2​(N0​)

A $2$ -Regular Sequence That Counts The Divisors of $n^{2} + 1$

Polynomials whose divisors are enumerated by $S L_{2} (N_{0})$