primitive semiperfect number
Parse the sequence of semiperfect numbers in ascending order, striking out any numbers that are divisible by any smaller number in the sequence. A number that remains after this process is then called a primitive semiperfect number or primitive pseudoperfect number. Put another way, none of the divisors
of a primitive semiperfect number are themselves semiperfect. The first few primitive semiperfect numbers are 6, 20, 28, 88, 104, 272, 304, 350, listed in A6036 of Sloane’s OEIS.
The list of the largest prime factors of each of the primitive semiperfect numbers gives the list of prime numbers almost in order but with many duplicates interspersed.
The smallest odd primitive semiperfect number is 945, which is also the smallest odd abundant number.
| Title | primitive semiperfect number |
|---|---|
| Canonical name | PrimitiveSemiperfectNumber |
| Date of creation | 2013-03-22 16:19:00 |
| Last modified on | 2013-03-22 16:19:00 |
| Owner | Mravinci (12996) |
| Last modified by | Mravinci (12996) |
| Numerical id | 5 |
| Author | Mravinci (12996) |
| Entry type | Definition |
| Classification | msc 11D85 |
| Synonym | primitive pseudoperfect number |
| Synonym | irreducible semiperfect number |