hyperperfect number
A hyperperfect number for a given is an integer such that , where is the sum of divisors function. is then called -hyperperfect. For example, 325 is 3-hyperperfect since its divisors (1, 5, 13, 25, 65, 325) add up to 434, and . Numbers that are 1-hyperperfect are by default called perfect numbers, since .
The 2-hyperperfect numbers are listed in A007593 of Sloane’s OEIS. As of 2007, the only known 3-hyperperfect number is 325. The two known 4-hyperperfect numbers are 1950625 and 1220640625, a sequence too short to list in the OEIS, and no 5-hyperperfect numbers are known to exist. The 6-hyperperfect numbers are listed in A028499.
References
- 1 Judson S. McCrainie, “A Study of Hyperperfect Numbers” Journal of Integer Sequences 3 (2000): 00.1.3
Title | hyperperfect number |
---|---|
Canonical name | HyperperfectNumber |
Date of creation | 2013-03-22 17:49:38 |
Last modified on | 2013-03-22 17:49:38 |
Owner | CompositeFan (12809) |
Last modified by | CompositeFan (12809) |
Numerical id | 4 |
Author | CompositeFan (12809) |
Entry type | Definition |
Classification | msc 11A05 |