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On some over primes

Abstract : It will be shown that, for any $\delta > 0$, \[ {\sum_{p\leq n}}^* \; \frac{\log p}{p} = \frac{1}{2} \log n + O\Big((\log n)^{\frac{5}{6}+\delta}\Big), \] where (*) restricts the summation to those primes $p$, which satisfy $n = kp+r$ for some integers $k$ and $r$, $p/2 < r < p$. This result is connected with questions concerning prime divisors of binomial coefficients.
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J W Sander. On some over primes. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 1994, Volume 17 - 1994, pp.32 - 39. ⟨10.46298/hrj.1994.129⟩. ⟨hal-01108738⟩

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