Odd perfect numbers, Diophantine equations, and upper bounds

We obtain a new upper bound for odd multiperfect numbers. If N is an odd perfect number with k distinct prime divisors and P is its largest prime divisor, we find as a corollary that 10^{12}P^{2}N

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Bibliographic Details
Published in:Mathematics of computation 2015-09, Vol.84 (295), p.2549-2567
Main Author: NIELSEN, PACE P.
Format: Article
Language:English
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Summary:We obtain a new upper bound for odd multiperfect numbers. If N is an odd perfect number with k distinct prime divisors and P is its largest prime divisor, we find as a corollary that 10^{12}P^{2}N
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-2015-02941-X