SEMIPERFECT NUMBER

In mathematics, a 'semiperfect number' or 'pseudoperfect number' is a natural number ''n'' that is equal to the sum of all or some of its proper divisors.
The first few semiperfect numbers are
:6, 12, 18, 20, 24, 28, 30, 36, 40, ... ;
every multiple of a semiperfect number is semiperfect, and every number of the form 2^''m''''p'' for a natural number ''m'' and a prime number ''p'' such that ''p'' < 2^{''m'' + 1} is also semiperfect.
The smallest odd semiperfect number is 945 (see, e.g., Friedman 1993).
A semiperfect number that is equal to the sum of all its proper divisors is called a perfect number; an abundant number which is not semiperfect is called a weird number. With one exception, all primary pseudoperfect numbers are semiperfect. Every practical number that is not a power of two is semiperfect.
A semiperfect number that is not divisible by any smaller semiperfect number is a primitive semiperfect number.

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★ MathWorld: Semiperfect number