C. S. Franze
Published 2011-11-08Version 1
We prove that there are infinitely many integers $n$ such that the total number of prime factors of $(n+h_{1})(n+h_{2})...(n+h_{\kappa})$ is at most $(1/2)\kappa\log\kappa+O(\kappa)$, provided $\kappa$ is sufficiently large.
Comments: 15 pages, submitted to London Mathematical Society
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