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\begin{abstract}
\noindent Let $N_{a,b}(x)$ count the number of primes $p\le x$ with $p$ 
dividing $a^k+b^k$ for some $k\ge 1$. It is known that 
$N_{a,b}(x)\sim c(a,b)x/\log x$ for some rational number $c(a,b)$ 
that depends in a rather intricate way on $a$ and $b$. A simple 
heuristic formula for $N_{a,b}(x)$ 
is proposed and it is proved that it is asymptotically exact, i.e.,
has the same asymptotic behavior as $N_{a,b}(x)$. Connections with
Ramanujan sums and character sums are discussed.
\end{abstract}


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