Noah Lebowitz-Lockard

activity

20162025

most citedA note on the number of Egyptian fractions

2 citations · 3 across the 9 of their papers we have counts for

collaborators

Showing 2024Show all

4 papers · 1 filter

math.CO2024

Partitions in which every term but the smallest one is consecutive

Rajat Gupta, Noah Lebowitz-Lockard

In this article, we introduce the notion of almost consecutive partitions. A partition is almost consecutive if every term is consecutive, with the possible exception of the smalle…

math.NT2024

On the $k$ th smallest part of a partition into distinct parts

Rajat Gupta, Noah Lebowitz-Lockard, Joseph Vandehey

A classic theorem of Uchimura states that the difference between the sum of the smallest parts of the partitions of $n$ into an odd number of distinct parts and the corresponding s…

math.NT2024

On the number of partitions of a number into distinct divisors

Noah Lebowitz-Lockard, Joseph Vandehey

Let $p_{dsd} (n)$ be the number of partitions of $n$ into distinct squarefree divisors of $n$ . In this note, we find a lower bound for $p_{dsd} (n)$ , as well as a…

math.NT2024

Runs of integers with constant values of the Carmichael function

Noah Lebowitz-Lockard, J. C. Saunders

In 2023, the first author and Vandehey proved that the largest $k$ for which the string of equalities $λ (n + 1) = λ (n + 2) = \dots = λ (n + k)$ holds for some $n \leq x$ , where $λ$ is the Carmi…

Partitions in which every term but the smallest one is consecutive

On the kth smallest part of a partition into distinct parts

On the number of partitions of a number into distinct divisors

Runs of integers with constant values of the Carmichael function

On the $k$ th smallest part of a partition into distinct parts