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.

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.