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 2n + 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.[1]
Numbers do exist where the sum of all the divisors σ(n) is equal to 2n + 2: 20, 104, 464, 650, 1952, 130304, 522752 ... (sequence A088831 in OEIS). Many of these numbers are of the form 2n−1(2n − 3) where 2n − 3 is prime (instead of 2n − 1 with perfect numbers)
Notes
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References
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Divisibility-based sets of integers
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| Aliquot sequence-related | ||
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