TY - UNPB
T1 - An Algorithm for Ennola’s Second Theorem and Counting Smooth Numbers in Practice
AU - Makdad, Chloe
AU - Sorenson, Jonathan P
N1 - Let $Ψ(x,y)$ count the number of positive integers $n\le x$ such that every prime divisor of $n$ is at most $y$. Given inputs $x$ and $y$, what is the best way to estimate $Ψ(x,y)$?
PY - 2022/8
Y1 - 2022/8
N2 - Given inputs x and y, what is the best way to estimate Ψ(x, y)? We address this problem in three ways: with a new algorithm to estimate Ψ(x, y) based on Ennola's second theorem [1969], with a performance improvement to an established algorithm, and with empirically based advice on how to choose an algorithm to estimate Ψ for the given inputs.
AB - Given inputs x and y, what is the best way to estimate Ψ(x, y)? We address this problem in three ways: with a new algorithm to estimate Ψ(x, y) based on Ennola's second theorem [1969], with a performance improvement to an established algorithm, and with empirically based advice on how to choose an algorithm to estimate Ψ for the given inputs.
UR - https://arxiv.org/abs/2208.01725
U2 - 10.48550/arXiv.2208.01725
DO - 10.48550/arXiv.2208.01725
M3 - Preprint
BT - An Algorithm for Ennola’s Second Theorem and Counting Smooth Numbers in Practice
ER -