Almost perfect number

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2020 Mathematics Subject Classification: Primary: 11A [MSN][ZBL]

Slightly defective number or least deficient number

A natural number $n$ such that the sum of all divisors of $n$ (the sum of divisors function $\sigma(n)$) is equal to $2n − 1$. The only known almost perfect numbers are the powers of 2 with non-negative exponents; however, it has not been shown that all almost perfect numbers are of this form. It is known that an odd almost perfect number greater than 1 would have at least 6 prime factors.

If $m$ is an odd almost perfect number then $m(2m-1)$ is a Descartes number.


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