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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 ...
The period of the sequence, or order of the set of sociable numbers, is the number of numbers in this cycle. If the period of the sequence is 1, the number is a sociable number of order 1, or a perfect number—for example, the proper divisors of 6 are 1, 2, and 3, whose sum is again 6.
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 ).
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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.
But one can also order them in columns corresponding to the number of moved elements = (sequence A098825 in the OEIS). Each entry in the table below on the left can be factored into two terms given in the table below on the right: the product of a binomial coefficient (given first in red ) and a subfactorial (given second in blue ).
Prices vary depending on seating section and number of days attending, and range from $10 to $55. Overall information on the 61st annual Merrie Monarch Festival can be found at.
The Fischer random chess numbering scheme can be shown in the form of a simple two-tables representation. Also a direct derivation of starting arrays exists for any given number from 0 to 959. This mapping of starting arrays and numbers stems from Reinhard Scharnagl and is now used worldwide for Fischer random chess.