Primitive semiperfect number


Primitive semiperfect number

In mathematics, a primitive semiperfect number (also called a "primitive pseudoperfect number", "irreducible semiperfect number" or "irreducible pseudoperfect number") is a semiperfect natural number that has no semiperfect proper divisor.

The first few primitive semiperfect numbers are 6, 20, 28, 88, 104, 272, 304, 350, ... (sequence [http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A006036 A006036] in OEIS).

There are infinitely many odd primitive semiperfect numbers (the smallest is 945,) as well as infinitely many primitive semiperfect numbers that are not harmonic divisor numbers.

External links

* [http://mathworld.wolfram.com/PrimitiveSemiperfectNumber.html MathWorld: Primitive semiperfect number]


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