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Hemiperfect number

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Hemiperfect number

In number theory, a hemiperfect number is a positive integer with a half-integral abundancy index.

For a given odd number k, a number n is called k-hemiperfect if and only if the sum of all positive divisors of n (the divisor function, σ(n)) is equal to k/2 × n.

Smallest k-hemiperfect numbers

The following table gives an overview of the smallest k-hemiperfect numbers for k ≤ 17 (sequence A088912 in the OEIS):

For example, 24 is 5-hemiperfect because the sum of the divisors of 24 is

1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 = 60 = 5/2 × 24.

References

Hemiperfect number Wikipedia


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