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Almost perfect numbers refer to numbers where

σ(x) = 2x - 1, where σ is the sum of divisors function. Any number in the form 2n is almost perfect because

σ(2n) = 1 + 2 + 4 + ... + 2n = 2n+1-1 = 2(2n) - 1.

It is unknown whether any other almost perfect numbers exist.

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Q: What numbers are almost perfect numbers?
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Related questions

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An almost perfect number is a natural number n such that the sum of all divisors of n is equal to 2n - 1.


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Perfect numbers are numbers where all the factors add to that number. For example 6's factors are 1,2, and 3 and 1+2+3=6. Therefore the next perfect number isn't until 28 which is 1,2, 4, 7, 14 where 1+2+4+7+14= 28 An almost perfect number is a number which, when adding all of its proper divisors (all divisors except himself), gives you one less, or one more then the number itlself. Up to now all known almost perfect numbers are 2^n. So to answer your question, the 2 almost perfect numbers between 5 and 20 are 8 and 16. Divisors of 8: 1,2,4 -----> 1+2+4=7 Divisors of 16: 1,2,4,8 -----> 1+2+4+8=15


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