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quasiperfect number
In mathematics, a quasiperfect number is a theoretical natural number ''n'' for which the sum of all its divisors (the divisor function ''σ''(''n'')) is equal to 2''n'' + 1. Quasiperfect numbers are abundant numbers.
No quasiperfect numbers have been found so far, but if a quasiperfect number exists, it must be an odd square number greater than 1035 and have at least seven distinct prime factors.
Numbers do exist where the sum of all the divisors ''σ''(''n'') is equal to 2''n'' + 2: 20, 104, 464, 650, 1952, 130304, 522752 ... . Many of these numbers are of the form 2''n''−1(2''n'' − 3) where 2''n'' − 3 is prime (instead of 2''n'' − 1 with perfect numbers)
==Notes==
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抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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