Primitive semiperfect number - Definition

In mathematics, a primitive semiperfect number (also called a primitive pseudoperfect number, irreducible semiperfect number or irreducible pseudoperfect number) is a natural number that has no semiperfect proper divisor.

The first few primitive semiperfect numbers are 6, 20, 28, 88, 104, 272, 304, 350, ... (sequence A006036 (http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A006036) in OEIS).

It has been shown that there exist infinitely many odd primitive semiperfect numbers, as well as infinitely many primitive semiperfect numbers that are not harmonic divisor numbers.

See also

• abundant number
• deficient number
• perfect number
• quasiperfect number

External links

• MathWorld: Primitive semiperfect number (http://mathworld.wolfram.com/PrimitiveSemiperfectNumber.html)