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 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.
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