Erdős problem 768

If $A(x)$ counts integers satisfying the Sylow divisor condition, determine the constant $c$ in $A(x)/x = \exp(-(c + o(1)) \sqrt{\log x} \log\log x)$ . The claimed exact value is $c = 1/(2\sqrt{\log 2})$ .

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Let $A(x)$ count $n \le x$ such that every prime $p \mid n$ has a divisor $d > 1$ of $n$ with $d \equiv 1 \pmod p$. Erdos asked whether $A(x)/x = \exp(-(c+o(1))\sqrt{\log x}\log\log x)$. It does, with $c = 1/(2\sqrt{\log 2})$.

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