Quasiperfect number
From Wikipedia, the free encyclopedia
In mathematics, a quasiperfect number is a theoretical natural number n for which the sum of all its divisors (the divisor function σ(n)) is equal to 2n + 1. Quasiperfect numbers are abundant numbers.
No quasiperfect numbers have been found so far, but if a quasiperfect number exists, it must be an odd square number greater than 1035 and have at least seven distinct prime factors. [1]
[edit] Notes
- ^ Hagis, Peter; Cohen, Graeme L. (1982). "Some results concerning quasiperfect numbers". J. Austral. Math. Soc. Ser. A 33 (2): 275–286. doi:10.1017/S1446788700018401. MR0668448.
[edit] References
- Brown, E.; Abbott, H.; Aull, C.; Suryanarayana, D. (1973). "Quasiperfect numbers". Acta Arithm. 22: 439-447. MR0316368. http://matwbn.icm.edu.pl/ksiazki/aa/aa22/aa2245.pdf.
- Kishore, Masao (1978). "Odd integers N with five distinct prime factors for which...". Math. Comput. 32: 303-309. MR0485658.
- Cohen, Graeme L. (1980). "On odd perfect numbers (ii), multiperfect numbers and quasiperfect numbers". J. Austral. Math. Soc. 29: 369-384. doi:10.1017/S1446788700021376. MR0569525.
- James J. Tattersall (1999). Elementary number theory in nine chapters. Cambridge University Press. pp. 147. ISBN 0521585317.
|
||||||||||||||||||||||
 |
This number theory-related article is a stub. You can help Wikipedia by expanding it. |
