Noah Lebowitz-Lockard

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math.NT2022★ 2 cited

A note on the number of Egyptian fractions

Noah Lebowitz-Lockard, Victor Souza

Refining an estimate of Croot, Dobbs, Friedlander, Hetzel and Pappalardi, we show that for all $k \geq 2$ , the number of integers $1 \leq a \leq n$ such that the equation $a/n = 1/…

math.NT2021

Distribution mod $p$ of Euler's totient and the sum of proper divisors

Noah Lebowitz-Lockard, Paul Pollack, Akash Singha Roy

We consider the distribution in residue classes modulo primes $p$ of Euler's totient function $ϕ (n)$ and the sum-of-proper-divisors function $s (n) := σ (n) - n$ . We prove that the value…

math.NT2021

On factorizations into coprime parts

Matthew Just, Noah Lebowitz-Lockard

Let $f (n)$ and $g (n)$ be the number of unordered and ordered factorizations of $n$ into integers larger than one. Let $F (n)$ and $G (n)$ have the additional restriction that the fac…

math.NT2018

Irreducible quadratic polynomials and Euler's function

Noah Lebowitz-Lockard

Let $P (x)$ be an irreducible quadratic polynomial in $Z [x]$ . We show that for almost all $n$ , $P (n)$ does not lie in the range of Euler's totient function.

A note on the number of Egyptian fractions

Distribution mod p of Euler's totient and the sum of proper divisors

On factorizations into coprime parts

Irreducible quadratic polynomials and Euler's function

Distribution mod $p$ of Euler's totient and the sum of proper divisors