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6 (six) is the natural number following 5 and preceding 7. It is a composite number and the smallest perfect number. In mathematics Six is the smallest positive integer which is neither a square number nor a prime number; it is the second smallest composite number, behind 4; its proper divisors are , and . Since 6 equals the sum of its proper divisors, it is a perfect number; 6 is the smallest of the perfect numbers. It is also the smallest Granville number, or \mathcal-perfect number. As a perfect number: *6 is related to the Mersenne prime 3, since . (The next perfect number is 28.) *6 is the only even perfect number that is not the sum of successive odd cubes. *6 is the root of the 6-aliquot tree, and is itself the aliquot sum of only one other number; the square number, . Six is the only number that is both the sum and the product of three consecutive positive numbers. Unrelated to 6's being a perfect number, a Golomb ruler of length 6 is a "perfect ruler". Six is a con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Senary
A senary () numeral system (also known as base-6, heximal, or seximal) has six as its base. It has been adopted independently by a small number of cultures. Like decimal, it is a semiprime, though it is unique as the product of the only two consecutive numbers that are both prime (2 and 3). As six is a superior highly composite number, many of the arguments made in favor of the duodecimal system also apply to senary. In turn, the senary logic refers to an extension of Jan Łukasiewicz's and Stephen Cole Kleene's ternary logic systems adjusted to explain the logic of statistical tests and missing data patterns in sciences using empirical methods. Formal definition The standard set of digits in senary is given by \mathcal_6 = \lbrace 0, 1, 2, 3, 4, 5\rbrace, with a linear order 0 < 1 < 2 < 3 < 4 < 5. Let be the Kleene closure of |
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