Berdellima, Arian
(2011):
*Perfect numbers - a lower bound for an odd perfect number.*

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## Abstract

In this work we construct a lower bound for an odd perfect number in terms of the number of its distinct prime factors. We further generalize the formula for any natural number for which the number of its distinct prime factors is known.

Item Type: | MPRA Paper |
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Original Title: | Perfect numbers - a lower bound for an odd perfect number |

Language: | English |

Keywords: | Perfect Numbers, Odd Perfect Numbers, Positive Divisors, Prime Factors, Lower Bound. |

Subjects: | A - General Economics and Teaching > A1 - General Economics > A19 - Other |

Item ID: | 31218 |

Depositing User: | Users 17400 not found. |

Date Deposited: | 01 Jun 2011 02:09 |

Last Modified: | 28 Sep 2019 04:30 |

References: | G.H.Hardy, E.M. Wright, An Introduction to the Theory of Numbers, Sixth Edition, Oxford University Press, 2008 (revised by D.R. Heath-Brown and J.H. Silverman). H. M. Edwards, Riemann Zeta Function, Dover Edition, 2001. J. Voight, Perfect Numbers: An Elementary Introduction, University of California, Berkley. Graeme L. Cohen, Even perfect numbers, Math. Gaz. 65 (1981), 28–30. L. E. Dickson, Notes on the theory of numbers, Amer. Math. Monthly 18 (1911), 109. Pace P. Nilesen, An Upper Bound for Odd Perfect Numbers, Integers 3: A14–A22. Pace. P. Nielsen, Odd perfect numbers have at least nine different prime factors, Math. Comp.76 (2007), no. 160, pp 2109–2126. D. R. Heath-Brown, Odd perfect numbers, Math. Proc. Camb. Phil. Soc. 115 (1994), 191-196. P. Jenkins, Odd perfect numbers have a factor that exceeds 107 , Math. Comp. 72 (2003), 1549-1554 D. E. Ianucci, The second largest prime divisor of an odd perfect number exceeds ten thousand, Math.Comp. 68 (1999), 1749-1760. D. E. Ianucci, The third largest prime divisor of an odd perfect number exceeds one hundred, Math.Comp. 69 (2000), 867-879. Mersenne prime search, http://www.mersenne.org/primes, 2011. Wolfram MathWorld, Perfect Numbers, http://mathworld.wolfram.com/PerfectNumber.html, 2011. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/31218 |