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A Semiperfect Number for which none of its Proper Divisors are pseudoperfect (Guy 1994, p. 46). The first few are 6, 20, 28, 88, 104, 272 ... (Sloane's A006036). Primitive pseudoperfect numbers are also called Irreducible Semiperfect Numbers. There are infinitely many primitive pseudoperfect numbers which are not Harmonic Divisor Numbers, and infinitely many Odd primitive semiperfect numbers.
See also Harmonic Divisor Number, Semiperfect Number
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 ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.