3-tuples have at most 7 prime factors infinitely often
Abstract
Let L1, L2 L3 be integer linear functions with no fixed prime divisor. We show there are infinitely many n for which the product L1(n)L2(n)L3(n) has at most 7 prime factors, improving a result of Porter. We do this by means of a weighted sieve based upon the Diamond-Halberstam-Richert multidimensional sieve.
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