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pseudoperfect numbers
A number    is called pseudoperfect if it is equal to the sum of a subset of its proper divisors.

For example, 12 is pseudoperfect since it can be written as 2+4+6.

Pseudoperfect numbers are also called semiperfect.

All pseudoperfect numbers are clearly perfect or abundant and all the practical numbers, except powers of 2, are also pseudoperfect.

The multiples of a pseudoperfect number are pseudoperfect and a number of the form    is surely pseudoperfect if there is a prime    which divides  .

According to Wenjie Fang, all the odd abundant number below    are also pseudoperfect.

An abundant number which is not pseudoperfect is called weird.

The first pseudoperfect numbers are 6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 48, 54, 56, 60, 66, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 176, 180 more terms

Below, the spiral pattern of pseudoperfect numbers up to  . See the page on prime numbers for an explanation and links to similar pictures.

Pseudoperfect numbers can also be... (you may click on names or numbers and on + to get more values)