Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-20T03:01:34.604Z Has data issue: false hasContentIssue false
  • English
  • Français

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: p.shiu@yahoo.co.uk
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Sierpiński, W., Sur les nombres pseudoparfaits, Mat. vesnik, 2 (17), (1965) pp. 212–213.Google Scholar
2. Shiu, Peter, Egyptian fraction representations of 1 with odd denominators, Math. Gaz., 93 (July 2009) pp. 271–275.Google Scholar
3. Hardy, G. H. and Wright, E. M., An introduction to the theory of numbers (4th edn), Clarendon Press (1960).Google Scholar
4. Baker, R. C. and Harman, G., The three primes theorem with almost equal summands, Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 356, No. 1738, (1998) pp. 763–780.10.1098/rsta.1998.0184CrossRefGoogle Scholar