C. Pomerance

activity

20042023

most citedThe iterated Carmichael λ-function and the number of cycles of the power generator

17 citations · 93 across the 37 of their papers we have counts for

collaborators

44 papers

math.NT2023

An inequality related to the sieve of Eratosthenes

Steve Fan, Carl Pomerance

Let $Φ (x, y)$ denote the number of integers $n \in [1, x]$ free of prime factors $\leq y$ . We show that but for a few small cases, $Φ (x, y) < .6 x / lo g y$ when $y \leq x$ .

math.NT2022

Permutations with arithmetic constraints

Carl Pomerance

Let $S_{lcm} (n)$ denote the set of permutations $π$ of $[n] = {1, 2, \dots, n}$ such that $lcm [j, π (j)] \leq n$ for each $j \in [n]$ . Further, let $S_{div} (n)$ denote the num…

math.NT2022

Coprime permutations

Carl Pomerance

Let $C (n)$ denote the number of permutations $σ$ of $[n] = {1, 2, \dots, n}$ such that $g cd (j, σ (j)) = 1$ for each $j \in [n]$ . We prove that for $n$ sufficiently large, $n!/3.73^n < C(n)…

math.NT2021

Coprime matchings

Carl Pomerance

We prove that there is a matching between 2 intervals of positive integers of the same even length, with corresponding pairs coprime, provided the intervals are in $[n]$ and their…

math.NT2021

On a nonintegrality conjecture

Florian Luca, Carl Pomerance

It is conjectured that the sum $S_{r} (n) = k = 1 \sum n \frac{k}{k + r} (k n)$ for positive integers $r, n$ is never integral. This has been shown for $r \leq 22$ . In this note…

math.NT2021

The denominators of the Bernoulli numbers

Carl Pomerance, Samuel S. Wagstaff

We study the asymptotic density of the set of subscripts of the Bernoulli numbers having a given denominator. We also study the distribution of distinct Bernoulli denominators and…