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Problem 757

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Stealthy Numbers

A positive integer $N$ is stealthy, if there exist positive integers $a$, $b$, $c$, $d$ such that $ab=cd=N$ and $a+b=c+d+1$.
For example, $36=4\times 9=6\times 6$ is stealthy.

You are also given that there are $2851$ stealthy numbers not exceeding ${10}^6$.

How many stealthy numbers are there that don’t exceed ${10}^{14}$?

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隐匿数

对于正整数$N$，若存在正整数$a$、$b$、$c$、$d$使得$ab=cd=N$且$a+b=c+d+1$，则称$N$为隐匿数 。
例如，$36=4\times 9=6\times 6$是一个隐匿数。

已知在不超过${10}^6$的范围内有$2851$个隐匿数。

在不超过${10}^{14}$的范围内，有多少个隐匿数？

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