MathDB

Find the smallest

\lambda \in \mathbb{R}

such that for all

n \in \mathbb{N}_+

, there exists

x_1, x_2, \ldots, x_n

satisfying

n = x_1 x_2 \ldots x_{2023}

, where

x_i

is either a prime or a positive integer not exceeding

n^\lambda

for all

i \in \left\{ 1,2, \ldots, 2023 \right\}

.
Proposed by Yinghua Ai

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