The Primitive semiperfect number reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Primitive semiperfect number

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.

Also see

• Perfect number
• Quasiperfect number
• Deficient number
• Abundant number

External links

• MathWorld: Primitive semiperfect number

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