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On the second largest prime divisor of an odd perfect number

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Analytic Number Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 899))

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References

  1. J. T. Condict, On An Odd Perfect Number's Largest Prime Divisor, Senior Thesis, Middlebury College, May 1978.

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  2. P. Hagis, Jr. and W.L. McDaniel, “On the Largest Prime Divisor of an Odd Perfect Number. II,” Math. Comp., v. 29, 1975, pp. 922–924.

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  3. H.-J. Kanold, “Untersuchungen Über ungerade vollkommene Zahlen,” J. Reine Angew. Math., v. 183, 1941, pp. 98–109.

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  4. H.-J. Kanold, “Folgerungen aus dem Vorkommen einer Gausschen Primazahl in der Primfaktorenzerlegung einer ungeraden vollkommenen Zahl,” J. Reine Angew. Math., v. 186, 1944, pp. 25–29.

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  5. T. Nagell, Introduction to Number Theory, Wiley, New York, 1951.

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  6. I. Niven, Irrational Numbers, Wiley, New York, 1956.

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  7. C. Pomerance, “The Second Largest Prime Factor of An Odd Perfect Number,” Math. Comp., v. 29, 1975, pp. 914–921.

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  8. D. Slowinski, “Searching For the 27th Mersenne Prime,” J. Recr. Math., v. 11, 1978–79, pp. 258–261.

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  9. G.C. Webber, “Non-existence of Odd Perfect Numbers of the Form \(3^{2_\beta } p^\alpha s_1^{2_{\beta _1 } } s_2^{2_{\beta _2 } } s_3^{2_{\beta _3 } }\),” Duke Math J., v. 18, 1951, pp. 741–749.

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Author information

Authors and Affiliations

  1. Temple University, 19122, Philadelphia, Pa.

    Peter Hagis Jr.

Authors
  1. Peter Hagis Jr.
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Editor information

Marvin I. Knopp

Additional information

With gratitude, respect and affection this paper is dedicated to Emil Grosswald, my teacher, my colleague and my friend.

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© 1981 Springer-Verlag

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Hagis, P. (1981). On the second largest prime divisor of an odd perfect number. In: Knopp, M.I. (eds) Analytic Number Theory. Lecture Notes in Mathematics, vol 899. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096466

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  • DOI: https://doi.org/10.1007/BFb0096466

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11173-3

  • Online ISBN: 978-3-540-38953-8

  • eBook Packages: Springer Book Archive

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