Asymptotically Exact Heuristics for Prime
Divisors of the Sequence
Korteweg-de Vries Instituut
Plantage Muidergracht 24
1018 TV Amsterdam
count the number of primes
. It is known that
for some rational number
that depends in a rather intricate way on
. A simple
heuristic formula for
is proposed and it is proved that it is asymptotically exact, i.e.,
has the same asymptotic behavior as
. Connections with
Ramanujan sums and character sums are discussed.
Full version: pdf,
Received February 14 2005;
revised version received February 24 2006.
Published in Journal of Integer Sequences July 7 2006.
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