irreducible pseudoperfect number | irreducible semiperfect number | primitive semiperfect number

A pseudoperfect number for which none of its proper divisors are pseudoperfect. The first few are 6, 20, 28, 88, 104, 272, ... (OEIS A006036). Primitive pseudoperfect numbers are also called primitive semiperfect numbers or irreducible pseudoperfect numbers. There are infinitely many primitive pseudoperfect numbers which are not harmonic divisor numbers, and infinitely many odd primitive pseudoperfect numbers.

harmonic divisor number | primary pseudoperfect number | pseudoperfect number