| Divisibility-based sets of integers |
| Form of factorization: |
| Prime number |
| Composite number |
| Powerful number |
| Square-free number |
| Achilles number |
| Constrained divisor sums: |
| Perfect number |
| Almost perfect number |
| Quasiperfect number |
| Multiply perfect number |
| Hyperperfect number |
| Superperfect number |
| Unitary perfect number |
| Semiperfect number |
| Primitive semiperfect number |
| Practical number |
| Numbers with many divisors: |
| Abundant number |
| Highly abundant number |
| Superabundant number |
| Colossally abundant number |
| Highly composite number |
| Superior highly composite number |
| Other: |
| Deficient number |
| Weird number |
| Amicable number |
| Friendly number |
| Sociable number |
| Solitary number |
| Sublime number |
| Harmonic divisor number |
| Frugal number |
| Equidigital number |
| Extravagant number |
| See also: |
| Divisor function |
| Divisor |
| Prime factor |
| Factorization |
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 1038 and have at least seven distinct prime factors. [1]
Notes
- ^ Hagis, Peter & Cohen, Graeme L., (1982). "Some results concerning quasiperfect numbers". J. Austral. Math. Soc. Ser. A 33: 275–286. doi:.
References
- James J. Tattersall (1999). Elementary number theory in nine chapters. Cambridge University Press. pp. 147. ISBN 0521585317.
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