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Pseudoperfect numbers with no small prime divisors

Published online by Cambridge University Press:  01 August 2016

Peter Shiu
Peter Shiu*
Affiliation:
353 Fulwood Road, Sheffield, South Yorkshire S10 3BQ e-mail: [email protected]
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Extract

A perfect number is a number which is the sum of all its divisors except itself, the smallest such number being 6. By results due to Euclid and Euler, all the even perfect numbers are of the form 2P-1(2p - 1) where p and 2p - 1 are primes; the latter one is called a Mersenne prime. Whether there are infinitely many Mersenne primes is a notoriously difficult problem, as is the problem of whether there is an odd perfect number.

Type
Articles
Information
The Mathematical Gazette , Volume 93 , Issue 528 , November 2009 , pp. 404 - 409
Copyright
Copyright © The Mathematical Association 2009

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References

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