Primitive Pseudoperfect Number

A pseudoperfect number for which none of its proper divisors are pseudoperfect (Guy 1994, p. 46). The first few are 6, 20, 28, 88, 104, 272, ... (OEIS A006036). Primitive pseudoperfect numbers are also called primitive semiperfect numbers (Guy 1994, p. 46) or irreducible pseudoperfect numbers. There are infinitely many primitive pseudoperfect numbers which are not harmonic divisor numbers, and infinitely many odd primitive pseudoperfect numbers.

REFERENCES:

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 46, 1994.

Sloane, N. J. A. Sequence A006036/M4133 in "The On-Line Encyclopedia of Integer Sequences."