| 词条 | Hemiperfect number | |||||||||||||||||||||||||||
| 释义 |
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 {{sfrac|k|2}} × n. Smallest k-hemiperfect numbersThe following table gives an overview of the smallest k-hemiperfect numbers for k ≤ 17 {{OEIS|A088912}}:
For example, 24 is 5-hemiperfect because the sum of the divisors of 24 is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 = 60 = {{sfrac|5|2}} × 24. See also
References1. ^1 {{cite web|url=http://www.numericana.com/answer/numbers.htm#multiperfect |title=Number Theory |publisher=Numericana.com |date= |accessdate=2012-08-21}} {{Divisor classes}}{{Classes of natural numbers}} 1 : Integer sequences |
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