Density bounds for Euler’s function
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- by Charles R. Wall PDF
- Math. Comp. 26 (1972), 779-783 Request permission
Abstract:
Let $\varphi$ be Euler’s function. Upper and lower bounds are presented for $D(x)$, the density of the integers $n$ for which $\varphi (n)/n \leqq x$. The bounds, for $x = 0(.01)1$, have an average spread of less than 0.0203.References
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F. Behrend, “Über ’numeri abundantes.’ II,” Preuss. Akad. Wiss. Sitzungber, v. 6, 1933, pp. 280-293.
- Mark Kac, Statistical independence in probability, analysis and number theory. , The Carus Mathematical Monographs, No. 12, Mathematical Association of America; distributed by John Wiley and Sons, Inc., New York, 1959. MR 0110114 C. Wall, Topics Related to the Sum of Unitary Divisors of an Integer, Ph.D. Dissertation, University of Tennessee, Knoxville, Tenn., 1970.
- Charles R. Wall, Phillip L. Crews, and Donald B. Johnson, Density bounds for the sum of divisors function, Math. Comp. 26 (1972), 773–777. MR 327700, DOI 10.1090/S0025-5718-1972-0327700-7
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Math. Comp. 26 (1972), 779-783
- MSC: Primary 10H25; Secondary 10L10
- DOI: https://doi.org/10.1090/S0025-5718-1972-0327701-9
- MathSciNet review: 0327701