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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.
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A Meertens number is a sociable Meertens number with =, and a amicable Meertens number is a sociable Meertens number with =. The number of iterations i {\displaystyle i} needed for F b i ( n ) {\displaystyle F_{b}^{i}(n)} to reach a fixed point is the Meertens function's persistence of n {\displaystyle n} , and undefined if it never reaches a ...
This is an accepted version of this page This is the latest accepted revision, reviewed on 17 January 2025. Observation that in many real-life datasets, the leading digit is likely to be small For the unrelated adage, see Benford's law of controversy. The distribution of first digits, according to Benford's law. Each bar represents a digit, and the height of the bar is the percentage of ...
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
In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of n-dimensional simplicial complexes.For the most reasonable finite-dimensional spaces (such as compact manifolds, finite simplicial complexes or CW complexes), the sequence of Betti numbers is 0 from some point onward (Betti numbers vanish above the dimension of a space), and they ...
A perfect totient number is an integer that is equal to the sum of its iterated totients. That is, we apply the totient function to a number n, apply it again to the resulting totient, and so on, until the number 1 is reached, and add together the resulting sequence of numbers; if the sum equals n, then n is a perfect totient number.