Hyperperfect Number
In mathematics, a k-hyperperfect number is a natural number n for which the equality n = 1 + k(σ(n) − n − 1) holds, where σ(n) is the divisor function (i.e., the sum of all positive divisors of n). A hyperperfect number is a k-hyperperfect number for some integer k. Hyperperfect numbers generalize perfect numbers, which are 1-hyperperfect.
The first few numbers in the sequence of k-hyperperfect numbers are 6, 21, 28, 301, 325, 496, ... (sequence A034897 in OEIS), with the corresponding values of k being 1, 2, 1, 6, 3, 1, 12, ... (sequence A034898 in OEIS). The first few k-hyperperfect numbers that are not perfect are 21, 301, 325, 697, 1333, ... (sequence A007592 in OEIS).
Read more about Hyperperfect Number: List of Hyperperfect Numbers, Hyperdeficiency
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