Primitive semiperfect number

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

The first few primitive semiperfect numbers are 6, 20, 28, 88, 104, 272, 304, 350, ... (sequence A006036 in OEIS)

There are infinitely many odd primitive semiperfect numbers (the smallest is 945), as well as infinitely many primitive semiperfect numbers that are not harmonic divisor numbers.

External links

• Weisstein, Eric W., "Primitive semiperfect number" from MathWorld.