Pacific Journal of Mathematics

On the distribution of numbers of the form $\sigma(n)/n$ and on some related questions.

P. Erdős

Article information

Source
Pacific J. Math., Volume 52, Number 1 (1974), 59-65.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102912212

Mathematical Reviews number (MathSciNet)
MR0354601

Zentralblatt MATH identifier
0291.10040

Subjects
Primary: 10K20

Citation

Erdős, P. On the distribution of numbers of the form $\sigma(n)/n$ and on some related questions. Pacific J. Math. 52 (1974), no. 1, 59--65. https://projecteuclid.org/euclid.pjm/1102912212


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References

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  • [2] H. Davenport, Uber numeri abundantes, ibid., (1934), 830-834.
  • [3] H. G. Diamond, The distributionof values of Euler'sPhi function, Proc. Symp. Pure Math., Amer. Math. Soc. XXIV, (1972), 63-75.
  • [4] For the relevant results see e.g. P. Erds, On additive arithmetical functions and applicationsto number theory, Proc. International Congress Math., Amsterdam, (1954), Vol. IV, 13-19, Nordhoff Groningen, 1956 and see also M. Kac, Probability methods in some problems of analysis and number theory, Bull. Amer. Math. Soc,55 (1949), 641- 655, and the book of Kubilius, Probabilistic methods in the theory of numbers, Amer. Math. Soc. Translations, Vol.11.
  • [5] P. Erds, On the smoothness of the asymptotic distribution of additivearithmetical functions,Amer. J. Math., 61 (1939), 722-725.
  • [6] P. Erds, On amicable numbers, Publ. Math. Debl., 4 (1955-56), 108-111.
  • [7] P. Erds,Some remarksabout additive and multiplicativefunctions,Bull. Amer. Math. Soc, 52 (1946), 527-537, see Theorem 3, p.529.
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  • [9] P. Erds,Remarks on number theory I and II, Acta Arith., 5 (1959), 23-33 and 171-177.
  • [10] A. S. Fainleib, Distribution of values of Euler's function,Mat.Zametki, 1 (1967), 645-652 = Math. Notes, 1 (1967), 428-432.
  • [11] B. Hornfeck and E. Wirsing, Uber dia Hdufigkeitvollkommener Zahlen, Math. Annalen, 133 (1957), 431-438, see also E. Wirsing, Bemerkungenzu der Arbeit uber vollkommene Zahlen, ibid., 139 (1959), 316-318.
  • [12] I. Schoenberg, Uber die asymptotische verteilung reeller Zahlen mod 1, Math. Z., 28 (1928), 171-199.
  • [13] M. M. Tjan, On the question of the distribution of values of the Eulerfunction <p(ri), Litovsk. Mat. Sb., 6 (1966), 105-119.