THE DISTRIBUTION OF INTEGERS WITH AT LEAST TWO DIVISORS IN A SHORT INTERVAL |
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| Authors: | Ford Kevin; Tenenbaum Gerald |
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| Institution: | 1 Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green St., Urbana, IL, 61801, USA
2 Institut Élie Cartan, Université Henri–Poincareé Nancy 1, B.P. 239, 54506 Vandœuvre-1ès-Nancy Cedex, France |
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| Abstract: | We estimate the density of integers which have more than onedivisor in an interval (y, z] with z  y + y/(log y)log 4 –1. As a consequence, we determine the precise range of z suchthat most integers which have at least one divisor in (y, z]have exactly one such divisor. |
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