A concavity problem in number theory
Glasgow mathematical journal, Tome 12 (1971) no. 1, pp. 10-11
Voir la notice de l'article provenant de la source Cambridge University Press
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. LetShow the existence or non-existence of an integer K such that, ifthenWe now show that such a K exists, and that in (2) there is strict inequality in each case.
Anderson, Ian. A concavity problem in number theory. Glasgow mathematical journal, Tome 12 (1971) no. 1, pp. 10-11. doi: 10.1017/S0017089500001075
@article{10_1017_S0017089500001075,
author = {Anderson, Ian},
title = {A concavity problem in number theory},
journal = {Glasgow mathematical journal},
pages = {10--11},
year = {1971},
volume = {12},
number = {1},
doi = {10.1017/S0017089500001075},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500001075/}
}
[1] 1.Anderson, I., Primitive sequences whose elements have no large prime factors, Glasgow Math. J. 10 (1969), 10–15. Google Scholar | DOI
[2] 2.Anderson, I., On the divisors of a number, J. London Math. Soc. 43 (1968), 410–418. Google Scholar | DOI
[3] 3.Lieb, E. H., Concavity properties and a generating function for Stirling numbers, J. Combinatorial Tlieory, 5 (1968), 203–206. Google Scholar | DOI
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