In anthropology, kinship is the web of social relationships that form an important part of the lives of most humans in most societies, although its exact meanings even within this discipline are often debated. Anthropologist Robin Fox states that "the study of kinship is the study of what man does with these basic facts of life–mating, gestation, parenthood, socialization, siblingship etc." Human society is unique, he argues, in that we are "working with the same raw material as exists in the animal world, but [we] can conceptualize and categorize it to serve social ends." These social ends include the socialization of children and the formation of basic economic, political and religious groups.
Kinship can refer both to the patterns of social relationships themselves, or it can refer to the study of the patterns of social relationships in one or more human cultures (i.e. kinship studies). Over its history, anthropology has developed a number of related concepts and terms in the study of kinship, such as descent, descent group, lineage, affinity/affine, consanguinity/cognate and fictive kinship. Further, even within these two broad usages of the term, there are different theoretical approaches.
In number theory, friendly numbers are two or more natural numbers with a common abundancy, the ratio between the sum of divisors of a number and the number itself. Two numbers with the same abundancy form a friendly pair; n numbers with the same abundancy form a friendly n-tuple.
A number that is not part of any friendly pair is called solitary.
The abundancy 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. Note that abundancy is not the same as abundance which is defined as σ(n) − 2n.
Abundancy may also be expressed as where denotes a divisor function with equal to the sum of the k-th powers of the divisors of n.
The numbers 1 through 5 are all solitary. The smallest friendly number is 6, forming for example the friendly pair 6 and 28 with abundancy σ(6) / 6 = (1+2+3+6) / 6 = 2, the same as σ(28) / 28 = (1+2+4+7+14+28) / 28 = 2. The shared value 2 is an integer in this case but not in many other cases. There are several unsolved problems related to the friendly numbers.
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