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A Simple Proof of a Theorem of Landau

1954
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Proceedings of the Edinburgh Mathematical Society
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Let a k {x) be the number of integers n^x which are the product of just k prime factors, so that and let TT k (x) be the number of such n for which all the p { are different. The behaviour of tt k (x) and a k (x) as x->co is given by

doi:10.1017/s0013091500021349
fatcat:joorx73gjnchxiep7l7t52tcri