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A lower bound on the number of rough numbers. (arXiv:1705.04831v2 [math.NT] UPDATED)
来源于:arXiv
Conceptually, a rough number is a positive integer with no small prime
factors. Formally, for real numbers $x$ and $y$, let $\Phi(x,y)$ denote the
number of positive integers at most $x$ with no prime factors less than $y$. In
this paper we establish the lower bound $\Phi(n,p)\geq \lfloor 2n/p \rfloor +1$
when $p\geq 11$ is prime and $n\geq 2p$. 查看全文>>