Abstract
This article is motivated by several questions posed in [3], which we can now at least partially answer.
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References
F. Behrend, On sequences of numbers not divisible one by another, J. London Math. Soc. 10 (1935), 42–44.
P. Erdös and R.R. Hall, On some unconventional problems on the divisors of integers, J. Austral. Math. Soc. Ser. A 25 (1978), 479–s485.
P. Erdös et G. Tenenbaum, Sur les fonctions arithmétiques liées aux diviseurs consécutifs, J. Number Theory 31 (1989), 285–311.
E. Fouvry et G. Tenenbaum, Entiers sans grand facteur premier en progressions arithmétiques, preprint.
H. Halberstam and K.F. Roth, Sequences (1966, Oxford University Press; 2nd ed. 1983, Springer).
D.R. Heath Brown, Consecutive almost primes, preprint.
A. Hildebrand, Integers free of large prime factors and the Riemann Hypothesis, Mathematika 31 (1984), 258–271.
A. Hildebrand, On a conjecture of Balog, Proc. Amer. Math. Soc. 95, n° 4 (1985), 517–523.
A. Hildebrand, On the number of positive integers ≤ x and free of prime factors y, J. Number Theory 22 (1986), 289–307.
A. Hildebrand and G. Tenenbaum, On integers free of large prime factors, Trans. Amer. Math. Soc. 296 (1986), 265–290.
M. Huxley, On the difference between consecutive primes, Inventiones Math. 15 (1972), 164–170.
A. Ivič and J.-M. De Koninck, On the distance between consecutive divisors of an integer, Canad. Math. Bull. 29 (2), (1986), 208–217.
E. Saias, Sur le nombre des entiers sans grand facteur premier, J. Number Theory 32 (1989), 78–99.
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Balog, A., Erdös, P., Tenenbaum, G. (1990). On Arithmetic Functions Involving Consecutive Divisors. In: Berndt, B.C., Diamond, H.G., Halberstam, H., Hildebrand, A. (eds) Analytic Number Theory. Progress in Mathematics, vol 85. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3464-7_6
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