The sum of \(\alpha^{\Omega(n)}\) over integers n\(\leq x\) with all prime factors between \(\alpha\) and y

DOI10.1016/0022-314X(84)90054-4zbMath0531.10045MaRDI QIDQ788029

Douglas Hensley

Publication date: 1984

Published in: Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

asymptotic behaviourlargest prime factorDickman-de Bruijn function

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Distribution of primes (11N05)

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Extreme sizes in Gibbs-type exchangeable random partitions ⋮ The two-parameter Poisson-Dirichlet point process ⋮ A pair of difference differential equations of Euler-Cauchy type ⋮ On the number of \(y\)-smooth natural numbers \(\leq x\) representable as a sum of two integer squares

Cites Work

• On a problem of Oppenheim concerning Factorisatio Numerorum
• Sur des formules de Atle Selberg
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