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Catalan–Dickson Conjecture
In mathematics, an aliquot sequence is a sequence of positive integers in which each term is the sum of the proper divisors of the previous term. If the sequence reaches the number 1, it ends, since the sum of the proper divisors of 1 is 0. Definition and overview The wiktionary:aliquot, aliquot sequence starting with a positive integer can be defined formally in terms of the divisor function, sum-of-divisors function or the aliquot sum function in the following way: \begin s_0 &= k \\[4pt] s_n &= s(s_) = \sigma_1(s_) - s_ \quad \text \quad s_ > 0 \\[4pt] s_n &= 0 \quad \text \quad s_ = 0 \\[4pt] s(0) &= \text \end If the condition is added, then the terms after 0 are all 0, and all aliquot sequences would be infinite, and we can conjecture that all aliquot sequences are limit (mathematics), convergent, the limit of these sequences are usually 0 or 6. For example, the aliquot sequence of 10 is because: \begin \sigma_1(10) -10 &= 5 + 2 + 1 = 8, \\[4pt] \sigma_1(8) - 8 &= 4 + ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
