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Quasi-sociable numbers or reduced sociable numbers are numbers whose aliquot sums minus one form a cyclic sequence that begins and ends with the same number. They are generalizations of the concepts of betrothed numbers and quasiperfect numbers. The first quasi-sociable sequences, or quasi-sociable chains, were discovered by Mitchell Dickerman ...
In a sociable sequence, each number is the sum of the proper divisors of the preceding number, i.e., the sum excludes the preceding number itself. For the sequence to be sociable, the sequence must be cyclic and return to its starting point. The period of the sequence, or order of the set of sociable numbers, is the number of numbers in this cycle.
In mathematics, the amicable numbers are two different natural numbers related in such a way that the sum of the proper divisors of each is equal to the other number. That is, s ( a )= b and s ( b )= a , where s ( n )=σ( n )- n is equal to the sum of positive divisors of n except n itself (see also divisor function ).
An alphabetic numeral system employs the letters of a script in the specific order of the alphabet in order to express numerals. In Greek, letters are assigned to respective numbers in the following sets: 1 through 9, 10 through 90, 100 through 900, and so on. Decimal places are represented by a single symbol.
The Wedderburn–Etherington numbers may be calculated using the recurrence relation = = = (+) + = beginning with the base case =. [4]In terms of the interpretation of these numbers as counting rooted binary trees with n leaves, the summation in the recurrence counts the different ways of partitioning these leaves into two subsets, and of forming a subtree having each subset as its leaves.
The highest used position is close to the order of magnitude of the number. The number of tally marks required in the unary numeral system for describing the weight would have been w. In the positional system, the number of digits required to describe it is only + = +, for k ≥ 0.
There are a finite number of natural numbers less than +, so the number is guaranteed to reach a periodic point or a fixed point less than +, making it a preperiodic point. This means also that there are a finite number of perfect digit-to-digit invariant and cycles for any given base b {\displaystyle b} .
The order of operations, that is, the order in which the operations in an expression are usually performed, results from a convention adopted throughout mathematics, science, technology and many computer programming languages. It is summarized as: [2] [5] Parentheses; Exponentiation; Multiplication and division; Addition and subtraction