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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, 697, ... , with the corresponding values of ''k'' being 1, 2, 1, 6, 3, 1, 12, ... . The first few ''k''-hyperperfect numbers that are not perfect are 21, 301, 325, 697, 1333, ... . List of hyperperfect numbers The following table lists the first few ''k''-hyperperfect numbers for some values of ''k'', together with the sequence number in the On-Line Encyclopedia of Integer Sequences (OEIS) of the sequence of ''k''-hyperperfect numbers: It can be shown that if ''k'' > 1 is an odd intege ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
