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A concavity problem in number theory
Published online by Cambridge University Press: 18 May 2009
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For any fixed value of x, let denote the set of all positive integers with exactly k prime factors counted according to multiplicity, each prime factor being ≦ x. In an earlier paper [1] in this journal we posed the following problem. Let
Show the existence or non-existence of an integer K such that, if
then
We now show that such a K exists, and that in (2) there is strict inequality in each case.
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- Copyright © Glasgow Mathematical Journal Trust 1971