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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 ...
where n > 1 is an integer and p, q, r are prime numbers, then 2 n × p × q and 2 n × r are a pair of amicable numbers. This formula gives the pairs (220, 284) for n = 2, (17296, 18416) for n = 4, and (9363584, 9437056) for n = 7, but no other such pairs are known. Numbers of the form 3 × 2 n − 1 are known as Thabit numbers.
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. A pair of amicable numbers is a set of sociable numbers of ...
A number that is not part of any friendly pair is called solitary. The abundancy index of n is the rational number σ(n) / n, in which σ denotes the sum of divisors function. A number n is a friendly number if there exists m ≠ n such that σ(m) / m = σ(n) / n. Abundancy is not the same as abundance, which is defined as σ(n) − 2n.
A sense of number has also been found in dogs. For example, dogs were able [26] to perform simple additions of two objects, as revealed by their surprise when the result was incorrect. It is however argued that wolves perform better on quantity discrimination tasks than dogs and that this could be a result of a less demanding natural selection ...
Canine terminology in this article refers only to dog terminology, specialized terms describing the characteristics of various external parts of the domestic dog, as well as terms for structure, movement, and temperament. This terminology is not typically used for any of the wild species or subspecies of wild wolves, foxes, coyotes, dholes ...
A pedigree chart is a diagram that shows the occurrence of certain traits through different generations of a family, [1] [2] most commonly for humans, show dogs, and race horses. [ citation needed ] Definition
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